In a small bowl, combine warm milk and sugar, then sprinkle the yeast over it. Allow the yeast to activate until it becomes foamy, about 5 minutes.
Pour the yeast mixture into a large mixing bowl. Add the softened butter, egg, salt, and 2 cups of flour. Mix on medium speed until the batter is smooth.
Gradually add the remaining flour until a soft dough forms. Increase mixer speed to medium-high, beating for an additional 2-3 minutes. The dough should be tacky yet not sticky; if it’s too sticky, add extra flour, one tablespoon at a time.
Lightly grease a large bowl and place the dough inside, turning it once to coat. Cover with a clean towel and let it rise in a warm area until doubled, approximately 45-60 minutes.
Once risen, gently punch down the dough. Lightly flour your work surface and turn out the dough. Knead lightly if needed, then allow it to rest for a few minutes while preparing the baking sheets with a silicone mat or non-stick spray.
Roll out the dough into a 12x8 inch rectangle, about ½ inch thick. Using a sharp knife, cut the dough into 24-30 even pieces.
Arrange the rolls on the prepared baking sheets, cover with a dish towel, and allow them to rise in a warm place until nearly doubled, another 45-60 minutes.
About 20 minutes before the rolls have finished rising, preheat your oven to 350°F.
Bake the rolls in the preheated oven for 12-15 minutes or until they are a golden brown color.
Remove from the oven and immediately brush the tops with melted butter.