In a large mixing bowl of a stand mixer, with the dough hook attached, mix together the yeast, sugar and warm water. Let the mixture rest for 10 minutes to allow the yeast to proof, or bubble.
While the yeast is proofing, combine the milk and butter in a microwave safe dish and heat for 2 minutes in the microwave to warm the milk and melt the butter. Let it cool slightly before adding it to the yeast.
Add the egg, salt, milk/butter, and 3 cups of flour to the yeast and mix until combined. Continue adding the flour, 1/2 cup at a time, until the dough pulls away from the sides of the bowl while mixing and is tacky.
Continue kneading for about 5 minutes. Cover the dough and let it rise for 1-1 1/2 hours.
Remove the dough from the bowl onto a clean and lightly greased surface and divide the dough into 14-16 equal portions. Form each portion into a ball and place 1-2 inches apart on a greased pan. Cover and rise 45 minutes or until doubled in size.
Bake at 350 degrees F for 12-18 minutes, or until golden brown. Remove the rolls from the pan onto a wire rack to cool. Enjoy warm!