In a mixing bowl, combine warm milk and sugar. Sprinkle active dry yeast over the mixture and let it sit for about 5-10 minutes, until foamy.
Add melted butter, salt, and egg to the yeast mixture. Stir to combine.
Gradually add in the flour, one cup at a time, mixing until a soft dough forms. If using a stand mixer, use a dough hook and mix on low speed until combined.
Knead the dough on a floured surface for about 5 minutes, or until smooth and elastic. If using a stand mixer, knead on low speed for about 3-4 minutes.
Place the dough in a greased bowl, cover it with a kitchen towel, and let it rise in a warm place for about 1 hour, or until it doubles in size.
Once the dough has risen, punch it down and turn it onto a floured surface. Divide the dough into 12 equal pieces, shape into balls, and place them on a greased baking sheet lined with parchment paper.
Cover the rolls with a kitchen towel and let them rise for another 30 minutes.
Preheat the oven to 350°F (175°C). Bake the rolls for 12-15 minutes or until golden brown.
Remove from the oven and immediately brush with melted butter.