Heat milk to 110 degrees. In the bowl of a stand mixer, combine yeast, sugar, salt, egg, butter, and milk.
Using the dough hook, on low speed, mix in 2 cups of flour. Scrape down the sides with a rubber spatula as needed.
Add additional flour, a quarter cup at a time, until the dough starts to pull away from the sides of the bowl.
Knead the dough on medium speed for about 5 minutes or knead by hand for 10 minutes. Let the dough rest for a few minutes, it should be smooth and elastic.
Transfer the dough to a lightly greased bowl and allow to rise until doubled in size, about 30 minutes.
Punch the dough down and divide into 12-15 equal sized balls. Place balls of dough into a lightly greased 9x13 baking dish and allow to rise until doubled in size, about 30 minutes.
Preheat oven to 350 degrees. Bake for 20 minutes or until the tops are golden brown.
Brush with melted butter.