Whisk together the warm milk, butter, and egg in the bowl of a stand mixer. Add flour and yeast and using the dough hook mix on low speed until all flour is moistened, about 2 minutes, scraping down the bowl as needed. Let stand for 15 minutes.
Add sugar and salt and mix on medium-low speed for 5 minutes or until dough is smooth (dough will stick to the bottom of the bowl). Transfer dough to a large, greased bowl. Cover tightly with plastic wrap and let rise at room temperature until doubled in size, about 1 hour.
Combine sugar, cinnamon, and salt in bowl. Reserve ¾ cup cinnamon sugar. Place remaining cinnamon sugar in shallow dish. Place 6 tablespoons melted butter in second shallow dish.
Grease 13 by 9-inch baking dish. Turn out dough onto counter and divide into fifteen portions (about 1 oz each). Place a portion of dough in your palm and roll against counter into smooth, tight ball. Repeat with remaining dough.
Roll each dough ball in melted butter in shallow dish, then roll in cinnamon sugar in shallow dish. Place dough balls in prepared dish in 3 rows of five into the prepared pan. Cover loosely with plastic and let rise at room temperature until doubled in size, about 1 hour (cinnamon sugar coating may crack during rising; this is OK). Adjust oven rack to middle position and heat oven to 350 degrees.
Bake until rolls are puffed and golden brown, about 25 minutes.
Whisk reserved cinnamon sugar and remaining 6 tablespoons melted butter in bowl until combined (mixture may look separated). Brush tops and sides of hot rolls with cinnamon sugar–butter mixture (use all of it) and let cool in dish for 10 minutes. Remove rolls from dish and serve warm. |