In a medium bowl, whisk together 1/2 cup (120 grams) warm water, warm milk, 2 tablespoons (28 grams) melted butter, and yeast. Let stand until foamy, 5 to 10 minutes.: As you mix, notice the slightly steamy warmth and that the liquid feels just tepid to the touch, which is perfect for yeast activation. After a few minutes you should see small bubbles and a foamy layer, an audible faint hiss or tiny fizz that signals live yeast. This step is crucial because without an active foam the dough will remain dense. A common mistake is using water that is too hot, which kills the yeast, or too cold, which delays proofing. If you don't see foam after ten minutes, discard and try with fresh yeast and properly warmed liquids.
In the bowl of a stand mixer fitted with the paddle attachment, beat flour, sugar, and salt at low speed until combined. Add yeast mixture and 1 egg (50 grams), and beat at medium-low speed for 2 minutes. Add zucchini, cheese, garlic powder, and thyme, and beat until well combined, about 1 minute, stopping to scrape sides of bowl.: The dry ingredients will mingle into a uniform pale mix, and you'll hear a soft, settling thud as the paddle moves through. This even distribution ensures the yeast and liquids meet a balanced matrix of flour and seasoning. Avoid over mixing here; forming the initial uniform mix prevents pockets of salt or sugar that could unevenly affect the dough.
Switch to the dough hook attachment. Beat at low speed until a soft, somewhat sticky dough forms, stopping to scrape sides of bowl, 6 to 8 minutes. (Dough should pass the windowpane test; see Note.) Turn out dough onto a very lightly floured surface, and gently shape into a ball.: As the wet and dry components merge, the batter will look shaggy and slightly tacky; you might smell a faint dairy sweetness from the milk and butter. This early mixing hydrates the flour and begins gluten alignment. The error to avoid is rushing to high speed which can overwork the dough prematurely, leading to tough texture.
Spray a large bowl with cooking spray. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 30 to 45 minutes.: The shredded zucchini will introduce moist flecks and the grated Parmesan cheese will sprinkle throughout, creating a speckled dough. You should catch the aromatic lift from the thyme and garlic, which hints at the finished flavor. Scrape the bowl so nothing clings to the sides; otherwise those bits will remain dry and unevenly distributed.
Spray a 9-inch springform pan with cooking spray.: When you change attachments, the machine will shift from a batter rhythm to a kneading cadence, a slower, rhythmic tug as the hook folds the dough. This sets up the gluten network. It's important to change tools rather than attempt long paddle kneading, because the hook better develops the chewy structure needed for rolls.
Divide dough into 14 portions (about 70 grams each). Using lightly floured hands, gently shape each portion into a smooth ball, and place in prepared pan. (Dough will fill pan.) Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 30 to 45 minutes.: Expect a transition where the dough gathers into a cohesive mass, slightly tacky but holding shape, and you'll hear a deeper, hollow sound as it pulls away from the bowl. This is where gluten forms, giving chew and structure. A useful check is the windowpane test; if the dough tears immediately, it needs more time. Avoid adding too much flour to dry it out, that will yield dense rolls instead of tender ones.
Preheat oven to 375°F (190°C).: The dough should feel springy and slightly warm from the friction of mixing, with a silky sheen from the butter. Shape it gently rather than punching, preserving the internal air pockets. Over handling here can deflate the dough, so be tender and patient.
In a small bowl, whisk remaining 1 egg (50 grams). Brush rolls with egg wash.: The greased bowl keeps the dough from sticking as it rises and helps you turn it easily to coat the dough surface. The scent of neutral spray is subtle but practical. If you skip greasing, dough can cling and tear when you try to turn it, which may damage the rise.
Bake until golden brown and an instant-read thermometer inserted in center registers 190°F (88°C), 25 to 30 minutes, rotating pan halfway through baking and covering with foil to prevent excess browning, if necessary. Immediately brush with remaining 2 tablespoons (28 grams) melted butter. Serve warm. Store in an airtight container for up to 4 days.: As you turn the dough, you should feel the soft surface pick up a thin sheen of butter from the bowl, sealing it and preventing a dry crust from forming. This helps the dough expand smoothly. If a skin forms, you can lightly mist with water to prevent drying, but avoid constant poking which can collapse the dough.
Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 30 to 45 minutes: During the rise you'll notice the dough expand visibly, the surface smoothing and the aroma becoming slightly yeasty and sweet. The room should be free of drafts to keep the temperature steady; even small cool breezes will slow the rise. Over proofing is a common error, which causes deflated rolls with poor oven spring, so check the doubling rather than only the clock.
Spray a 9-inch springform pan with cooking spray: A lightly greased pan ensures the rolls release cleanly after baking, the metal will conduct heat evenly creating even browning. If you skip this step, rolls can stick and tear when removed, so take the extra minute to prepare the pan properly.
Divide dough into 14 portions (about 70 grams each): As you portion, enjoy the soft, pillowy consistency; each piece should feel uniform in weight for even baking. Rolling into smooth balls creates tension on the surface that promotes a fine crumb and attractive rise. A frequent mistake is creating uneven sizes, which bakes unevenly; use a scale if possible for consistency.
Using lightly floured hands, gently shape each portion into a smooth ball, and place in prepared pan: The light flouring prevents sticking while you coax a glossy, taut ball that will rise upward. Placing them snugly in the pan helps them support one another for a soft pull apart texture. Pressing too hard flattens the tension and results in flat tops, so be gentle.
Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 30 to 45 minutes: The second rise develops the final airy pockets and adds volume; you'll see the rolls push against each other and the dough surface become pillowy. Keep the environment stable and check visually for doubling, as over rising will cause poor structure and collapse during baking.
Preheat oven to 375°F (190°C): The oven should reach temperature so the rolls get immediate oven spring, creating a tender interior and golden crust. You might hear faint pops from heating elements and smell a neutral warm air before baking. Baking in an under heated oven will make the rolls dense and pale, lacking proper rise and color.
In a small bowl, whisk remaining 1 egg (50 grams): The egg wash will create that glossy, golden finish; whisk until uniform and slightly frothy. Brush evenly to avoid mottled browning. If you forget the egg wash, the rolls will still bake but the tops will be matte and less visually inviting.
Brush rolls with egg wash: As you paint each roll, note how the surface accepts the wash and begins to gleam. The egg promotes browning and helps any topping adhere. Be careful not to pool the wash between rolls, which can create uneven coloring or gummy patches.
Bake until golden brown and an instant-read thermometer inserted in center registers 190°F (88°C), 25 to 30 minutes, rotating pan halfway through baking and covering with foil to prevent excess browning, if necessary: During baking you'll smell rich butter and roasted cheese, and see the tops turn a warm golden brown. Rotate the pan for even color and watch for rapid darkening at the edges. If the rolls brown too quickly, tent with foil to finish cooking without burning. A common misstep is underbaking, leaving a gummy center, so use the thermometer rather than relying solely on color.
Immediately brush with remaining 2 tablespoons (28 grams) melted butter: Brushing adds a final layer of shine and a buttery aroma that invites tasting. The extra butter also softens the crust slightly for an irresistible tender bite. If you skip this, the crust will be less rich and slightly drier to the touch.
Serve warm: Warm rolls showcase the melty cheese pockets and tender crumb best; you'll hear soft tearing sounds when pulled apart and taste the fresh herb notes. If you plan to store them, allow to cool slightly before sealing to avoid condensation, which can make them soggy.
Store in an airtight container for up to 4 days: Stored properly, these retain moisture and flavor, and reheating briefly restores that just baked sensation. Refrigeration can dry them, so I prefer airtight at room temperature for short term, or freezing for longer storage. Avoid leaving them uncovered which dries the crust and dulls the flavors.