Warm milk and butter until about 110 F.
Stir in yeast and sugar; let activate until foamy, about 10 minutes.
Mix flour, salt, and egg in a large bowl; add yeast mixture and stir into a soft dough.
Turn dough onto a lightly floured surface and knead until smooth, about 8 minutes.
Place dough in a greased bowl, cover, and let rise until doubled, about 60 minutes.
Punch down dough, divide into 12 portions, shape into balls, and arrange in a greased 9×13 pan; let rise 20 minutes.
Brush rolls with melted butter and bake at 375 F for 20 minutes, until golden.