In a large mixing bowl, whisk together the flour, sugar, yeast, and salt.
Add the warm milk, melted butter, and egg to the dry ingredients. Mix until a soft dough forms.
Knead the dough by hand or with a stand mixer for about 8–10 minutes, until it is smooth and elastic. Add a little more flour if the dough is too sticky.
Transfer the dough to a greased bowl, cover it, and let it rise in a warm place for 1 hour or until it has doubled in size.
Punch down the dough and divide it into 12 equal pieces. Shape each piece into a smooth ball.
Place the rolls in a greased 9×13-inch baking dish. Cover loosely and let them rise again for 30–45 minutes, until they are puffy.
Preheat the oven to 375°F (190°C).
Bake for 15–18 minutes, or until the tops are golden brown.
Immediately brush the warm rolls with melted butter and let them cool slightly before serving.