In a large bowl, mix the flour, the sugar, salt, and yeast together until evenly dispersed. Set aside. In a small microwavable bowl, heat the water, milk, and butter together in the microwave until the butter is melted (about 30-45 seconds). Stir the butter mixture into the flour mixture. Add the egg and knead with hand or with stand mixer for 3-4 minutes or until the dough is no longer sticky. Place in a lightly greased bowl and let rest for about 5 minutes.: The moment you combine the warm liquid with the dry flour you will smell a faint toasty sweetness, and the dough will begin to feel cohesive and slightly tacky. Mixing evenly ensures each pinch of dough has a bit of yeast and salt, which makes for an even rise. When kneading, listen for the quiet shift in texture as the dough becomes smoother, and you will see it pull away from the bowl sides. The five minute rest allows the gluten to relax so rolling is easier, which is especially helpful in a quick recipe. A common mistake is overheating the liquid, which can kill the yeast, so test the warmth with your finger it should be warm but not hot. If the dough still clings to your hands after kneading, sprinkle a touch more flour to avoid overworking it.
Preheat the oven to 200 degrees and turn off after 10 minutes or just before placing rolls in oven.: You will create a gentle, warm environment for the rolls to proof without rushing the yeast into collapse. The slight humidity and warmth coax the dough to puff up softly, which is key for a tender interior. When you open the oven door after the ten minutes you should feel a comfortable warmth that is noticeably milder than baking heat. Avoid setting the oven too hot or leaving it on as that drives rapid rise and then collapse, resulting in dense rolls. If your kitchen is already very warm, skip the oven proofing and let them rise at room temperature for the same period.
After the dough has rested for 5 minutes, roll it out in a 15×9 inch rectangle. Spread the softened butter on top. Mix together the cinnamon and sugar and sprinkle it all over the dough. Roll up the dough tightly and cut into 9 (large) even pieces. Place in a lightly greased 9-inch or square pan (or cut into 12 small pieces and place in a 9×13 pan) and lightly cover with aluminum foil or plastic wrap.: Rolling the dough thin and even creates uniform layers that bake consistently into soft spirals. When you spread the softened butter , the dough should feel cool yet pliable, and the filling should appear as a thin, even blanket over the surface. As you roll, keep a light, steady pressure so the log is tight without squeezing out the filling. Cutting cleanly with a sharp knife or unflavored floss gives neat spiral edges. A frequent error is rolling unevenly, which produces some rolls thicker and undercooked while others brown too fast, so check the rectangle dimensions as you roll. If the butter oozes out, it may have been too soft; chill briefly and continue.
Place the cinnamon buns in the oven to rise for 20 minutes (with the oven off). After 20 minutes, keep the buns in the oven (REMOVE THE FOIL OR PLASTIC) and turn on the oven to 375 F. Bake the cinnamon rolls for an additional 15-20 minutes or until golden. Remove from oven and top with glaze.: During the passive 20 minute rise you will notice the buns gain volume and become pillowy to the touch, and the cinnamon aroma will intensify. Removing the cover before turning the oven on prevents trapped steam from making the tops soggy, and the instant switch to 375 F creates that golden surface while preserving a soft interior. Watch for a warm honey color developing on the tops, and when you jostle the pan gently the rolls should feel set but springy. A common pitfall is overbaking which dries the centers, so check at 15 minutes and remove once golden. If the tops brown too quickly, tent with foil briefly.
Mix the powdered sugar, vanilla, and 2 tablespoons milk together until smooth and lump free. Drizzle over warm rolls.: The glaze comes together silky and glossy, and when you drizzle it over hot rolls it will melt slightly and form a sweet sheen that seeps into the edges. Whisk until you see no specks or lumps, and adjust with the extra milk a teaspoon at a time until it pours slowly like thick cream. The warm rolls will steam as you glaze them, giving a lovely glossy finish that looks inviting and tastes decadent. Avoid making the glaze too runny or it will pool excessively; if that happens, whisk in a touch more powdered sugar to thicken. Slice into the rolls while warm to appreciate the gooey center and the contrast of tender dough and sweet glaze.
