Proof Yeast: In a small bowl, stir together yeast, warm water and 1/2 teaspoon sugar. Set aside for 5 minutes to 'proof'. (If the mixture doesn't get foamy on top, either the yeast is bad or the water was too hot). For instant yeast, add yeast, water and sugar with everything in step 2.: The bowl should smell faintly yeasty and the surface should become foamy within a few minutes, showing the yeast is alive, which matters for a reliable rise. If you do not see foam, do not proceed, as dough made with inactive yeast will remain dense, a common mistake to avoid.
Make Dough: Add the yeast mixture, warm milk, sugar, melted butter, salt and egg to a large bowl or stand mixer. Add 2 cups of flour and mix until smooth. Add an additional cup of flour and knead until combined. Slowly add more flour as needed, until the dough begins to pull away from the sides and bottom of the bowl. Knead it for about 5 minutes. The dough should be very soft and not overly sticky. Add more flour if needed.: Once mixed, the dough will feel soft and slightly tacky but should pull away from the bowl, a sign that gluten has developed enough. When kneading, you should hear a faint rhythm as the dough stretches and relaxes, and the texture moves from shaggy to silky, which helps create open, tender crumb after baking; avoid adding too much flour early, which can make the rolls dry.
First Rise: Place dough in a well-greased bowl, cover with a dry kitchen towel and let rise until doubled, about 1 1/2 hours. Meanwhile, butter a rimmed bakers half sheet (18×13") or a 9×13" pan. Set aside.: The dough will puff and double, filling the bowl with a buoyant, springy feel; touch it gently and it should slowly spring back. This rest period builds flavor and structure, so rushing it will result in denser rolls, a trap I've seen many fall into.
Roll out and Fill: Dust a work surface lightly with flour, or spray with non-stick cooking spray. Punch down the risen dough and roll it out into about a 20"x 18" rectangle. Spread 6 tablespoons softened butter on top. Mix sugar and cinnamon together and sprinkle over buttered dough, leaving 1/2 inch border. Sprinkle with walnuts, pecans, or raisins if desired.: Rolling the dough into a large rectangle should reveal an even, smooth surface, and the act of spreading softened butter will leave a glossy sheen that helps the cinnamon sugar stick; the filling should look evenly distributed, because uneven filling causes lopsided rolls when sliced.
Cut: Beginning on the 18-inch side, roll up dough tightly into a log. Pinch the ends together to seal. Cut into 12 equal portioned pieces (about 1 1/2 inches wide). A sharp serrated knife or a piece of floss work well to cut the dough.: When you slice the log into 12 pieces, each cross section should show a clear spiral. Use a serrated knife or floss to avoid squashing the log, because compressed rolls will lose their airy layers, which is a frequent mistake when using a dull knife.
Second Rise: Arrange rolls on prepared baking sheet and cover with a dry kitchen towel. Rise again for about an hour, until doubled in size. Preheat oven to 375 degrees F.: During this rise the rolls should visibly swell and the swirls should loosen into plump, soft mounds; the surface will look pillowy and slightly jiggly when nudged. Preheating the oven during this time ensures a consistent oven spring, missing which may cause underbaked centers.
Bake: Uncover rolls and bake for 18-22 minutes or until no longer doughy in the center. While the cinnamon rolls bake, make the icing.: In the oven the rolls will turn a warm golden brown and the sugar will bubble slightly at the edges, releasing a caramel scent that fills the kitchen. Remove them when they are set but still soft in the center, because overbaking dries them out, a common pitfall when baking larger trays.
Glaze: Mix butter and powdered sugar together for several minutes. Mix in vanilla and enough milk to reach a soft frosting consistency. (See notes for cream cheese frosting option). Spread over warm baked cinnamon rolls.: The glaze should be smooth and pourable, and when spread over warm rolls it will melt into the crevices, creating glossy ribbons of sweetness; if the glaze is too thin it will run off, so hold back milk until you reach a thick, spreadable consistency.