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.
Place in lightly greased bowl, cover, and let raise in warm place until doubled (about 1 hour).
Turn dough out onto lightly floured surface, punch down to get out air bubbles, and shape into rolls, placing rolls onto 2 lightly greased baking sheets. Cover with waxed paper and let rise for another 45 minutes to 1 hour.
Brush tops of buns with melted butter. Cover and let rise in a warm place until doubled, about 1 hour.
Preheat oven to 350 degrees F (175 degrees C).
Bake in preheated oven until lightly browned, 10 to 15 minutes.
