Preheat the oven to 350°F.
In the bowl of a stand mixer fitted with a dough hook, combine the warm milk, egg, melted butter, sugar, salt, flour, and instant yeast.
Mix on low speed until a shaggy dough forms, then increase to medium-low speed and knead for 8 to 10 minutes. The dough should become smooth, soft, and elastic. If it's too sticky, add flour one tablespoon at a time.
Transfer the dough to a lightly greased bowl. Cover with plastic wrap or a clean kitchen towel and let rise in a warm place for about 1 to 1½ hours, or until doubled in size.
Punch down the dough and turn it onto a lightly floured surface. Divide it into 12 equal pieces.
Shape each piece into a smooth ball by pulling the edges underneath and rolling gently between your hands.
Arrange the rolls in a greased 9x13-inch baking dish so they are just touching. Cover and let rise again for 30 to 45 minutes, until puffy.
Bake for 20 to 22 minutes, or until the tops are golden brown.
Brush the warm rolls with melted butter, if desired, and let cool for about 10 minutes before serving.