Combine milk, sugar, butter, and salt in small saucepan over medium heat; cook and stir until butter melts.
Remove from heat and allow to cool to lukewarm.
Combine 1 cup bread flour, egg, yeast, and milk mixture in the bowl of a stand mixer fitted with a dough hook; beat at lowest speed for 1 minute. Let rest 5 to 10 minutes. Add 2 3/4 cups bread flour; mix at next-to-lowest speed until dough cleans sides of bowl and sticks to dough hook, about 2 minutes.
Turn dough out onto lightly floured surface. Separate into 2 pieces, placing rolls onto 2 lightly greased baking sheets.
Divide into 4-6 balls and form into circles about 4" diameter.
Cover with waxed paper and let rise for 1 hour.
Preheat oven to 400 degrees.
Brush tops of buns with melted butter. Bake in preheated oven until lightly browned, 10 to 15 minutes.