In a large bowl, stir together the warm milk, sugar and yeast. Whisk in the egg and the 1/4 cup melted butter.
Add the salt and 3 cups of the flour and stir until a shaggy dough forms. Add the remaining 1/2 cup flour a little at a time.
Knead on a lightly floured surface for 6 to 8 minutes (or 5 minutes with a dough hook) until smooth, soft and only slightly tacky.
Place the dough in a greased bowl, cover and let rise in a warm place for 1 to 1 1/2 hours, until doubled.
Punch the dough down, divide into 12 equal pieces (about 70 g each) and roll into smooth balls. Place in a greased 9x13-inch pan.
Cover and let rise for 30 to 45 minutes, until puffy. Meanwhile, heat the oven to 375°F (190°C).
Bake for 18 to 22 minutes, until golden brown and the center of a roll reads about 190°F.
Brush the hot rolls with 2 tablespoons melted butter. Cool for 5 minutes and serve warm.