In a small bowl, combine the milk and sugar. Then sprinkle the yeast over the mixture and let it sit until it foams up about 5 minutes.
Put the yeast mixture in a large bowl and stir in the butter, egg, salt, and 2 cups of flour.
Be sure to beat at a medium speed until the batter is smooth.
Gradually add more flour until a soft dough forms. Increase the mixer speed to medium-high and beat for 2–3 minutes. The dough should be tacky but not sticky. If it’s too sticky, add more flour, 1 tablespoon at a time.
Lightly grease a large bowl and place the dough inside, turning it once to coat it with oil.
Cover the bowl with a clean dish towel and let the dough rise in a warm place until it doubles in size, about 45–60 minutes.
Gently punch down the dough. Lightly flour a work surface and turn the dough out onto it. Knead lightly if needed.
Let the dough rest for a few minutes while you prepare baking sheets with a silicone mat or non-stick cooking spray.
Roll the dough into a 12x8-inch rectangle, about ½-inch thick.
Cut the dough into 24–30 even pieces using a sharp knife.
Transfer the dough pieces to the prepared baking sheets. Cover with a dish towel and let them rise in a warm place until almost doubled in size, about 45–60 minutes.
About 20 minutes before the rising is complete, preheat the oven to 350°F (175°C).
Bake the rolls for 12–15 minutes, or until they are golden brown.
Remove the rolls from the oven and brush them with melted butter. Serve warm.