In a large mixing bowl, whisk together the flour, sugar, salt, and yeast.
Add the warm milk, melted butter, and egg to the dry ingredients. Mix until a sticky dough forms.
Knead the dough on a floured surface for 8-10 minutes, or until smooth and elastic. You can also use a stand mixer with a dough hook for 5-6 minutes.
Place the dough in a greased bowl, cover it with a damp cloth, and let it rise in a warm place for 1-1.5 hours, or until it has doubled in size.
Punch down the dough and divide it into 16 equal pieces. Shape each piece into a ball.
Place the dough balls in a greased Dutch oven in a circular pattern. Cover the Dutch oven with the lid and let the rolls rise again for 30-40 minutes, or until puffy.
Preheat your oven to 375°F (190°C).
Brush the tops of the rolls with more melted butter.
Bake in the Dutch oven (covered) for 15 minutes. Then, remove the lid and bake for an additional 10-12 minutes, or until golden brown.
Allow to cool slightly before serving.