Combine 2 cups flour, sugar, dry yeast and salt in a large mixer bowl and stir until blended. Combine milk, water and butter in a microwave-safe bowl. Microwave on HIGH in 15 second increments until very warm but not hot to the touch (120° to 130°F. Butter won’t melt completely). Add to flour mixture with egg.: Right away you will notice the warm, slightly sweet aroma from the milk and butter melding with the yeast dusting, which signals gentle activation. I like to run the mixer on low to incorporate the warm liquid slowly so the flour hydrates evenly, creating a tacky batter that will become dough. Watch the temperature carefully, because too hot liquid can kill the yeast and yield a flat loaf; if the bowl feels hotter than warm, let it cool a bit. A common mistake is using water that is too hot, so test it on your wrist before adding. The initial mixture should feel slightly warm and fragrant, not steam hot.
Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add 1 cup flour; beat 2 minutes at high speed, scraping bowl occasionally. Stir in just enough remaining flour so that the dough will form into a ball.: As you beat, the mixture shifts from a batter into a more cohesive mass, and you will hear the mixer change tone as the gluten begins to form. Scraping keeps pockets of dry flour from forming, which ensures consistent texture. When the mass cleans the bowl sides and gathers around the paddle or hook, that indicates you are close to the proper hydration. A common error is adding all the flour at once, which can lead to a dry, stiff dough; instead, add gradually until the dough forms a smooth, slightly tacky ball. The dough should feel springy and hold shape when lifted.
Knead on lightly floured surface until smooth and elastic and dough springs back when lightly pressed with 2 fingers, about 6 to 8 minutes. Cover with a towel; let rest for 10 minutes.: While kneading you will notice the dough becoming silkier and more homogeneous, with faint resistance as gluten strengthens. Pressing two fingers in should leave a gentle indentation that quickly bounces back, a sign of adequate development. Resting allows the gluten to relax, making the dough easier to shape. Avoid overflouring the surface, since extra flour dries the dough and can create a denser crumb. If the dough is sticky after 8 minutes, let it rest covered, which often resolves tackiness as the flour fully hydrates.
For filling, combine sugar and cinnamon in a shallow bowl.: The mixture should smell intensely of warm spice, and you will see even specks of cinnamon throughout. Mixing the sugar and cinnamon thoroughly ensures every bread piece will have consistent flavor intensity, so take a moment to blend them well. A common slip is using too coarse sugar which may not adhere well; finer sugar works better for a clingy coating. Keep the bowl nearby when you begin shaping so you can work quickly and evenly.
Cut dough into 36 pieces. Dip each piece into the melted butter and then roll in the cinnamon sugar mixture. Place in fluted tube pan that has been generously sprayed with cooking spray. Combine any remaining butter and sugar and drizzle over rolls. Cover with towel; let rise in warm place until doubled in size, about 45 minutes.: As you cut and dip, you will feel the dough give slightly as it yields to shaping, and the butter will make each piece glossy, which helps the cinnamon sugar cling and caramelize. Arranging the pieces snugly in the pan creates points of contact that lead to those delightful pull apart edges. During the rise watch for the dough to nearly double and become puffy and soft, with a light sheen; that indicates proper proof. Underproofing yields dense centers, while overproofing can collapse in the oven, so avoid extremes. If your kitchen is cool, place the pan near a warm oven or covered with a slightly warm towel to maintain consistent warmth.
Bake in preheated 375ºF oven for 25 to 30 minutes or until rolls are golden brown. Cool 5 minutes in pan, then invert on serving plate.: While baking, the kitchen will fill with a rich, toasty cinnamon aroma and the top will develop a golden, slightly glossy crust where the sugars caramelize. I look for an even golden color and a hollow sound when tapped lightly on top as cues of doneness. Letting it cool briefly in the pan stabilizes the structure so the loaf keeps form when inverted. Removing too early can cause collapse, so resist the urge to cut immediately. If the top browns too quickly, tent with foil to prevent burning while the interior finishes baking.
For glaze: Beat cream cheese and butter with a mixer until creamy. Stir in powdered sugar, milk, vanilla and salt. Mix until well combined. If a thinner consistency is desired, add additional milk, one tablespoon at a time. If a thicker consistency is desired, add more powdered sugar, one tablespoon at a time. Drizzle over bread or serve on the side for dipping. Store any remaining glaze in the refrigerator.: Beat cream cheese and butter with a mixer until creamy. Stir in powdered sugar, milk, vanilla and salt. Mix until well combined. If a thinner consistency is desired, add additional milk, one tablespoon at a time. If a thicker consistency is desired, add more powdered sugar, one tablespoon at a time. Drizzle over bread or serve on the side for dipping. Store any remaining glaze in the refrigerator. : The glaze should be glossy and velvety, with a tangy lift from the cream cheese that contrasts the sweet bread. When you drizzle it, it should flow slowly and cling to edges, creating ribbons of sweetness. If the glaze feels gritty, beat it longer or sift the powdered sugar first for a smoother finish. Over thinning makes it run off the loaf quickly, while too thick a glaze will sit like paste, so balance carefully. Refrigerate leftovers to keep the glaze safe, and let it come back to room temperature if you want it more pourable before serving.