Activate the Yeast: In a small bowl, combine the warm milk and sugar. Sprinkle the yeast over the top and let it sit until foamy, about 5 minutes.
Mix the Dough: In a large mixing bowl, add the yeast mixture, ¼ cup butter, egg, salt, and 2 cups of flour. Beat the mixture on medium speed until the batter is smooth. Gradually add the remaining flour until a soft ball of 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 is too sticky, add more flour, 1 tablespoon at a time.
Let the Dough Rise: Lightly grease a large bowl and place the dough in it, turning once to coat. Cover with a clean dish towel and let it rise in a warm place until doubled in size, about 45-60 minutes.
Prepare the Dough: Punch the dough down gently. Lightly flour your work surface and turn the dough out of the bowl. Knead lightly if necessary, then let it rest for a few minutes while you prepare baking sheets by lining them with a silicone mat or spraying with non-stick cooking spray.
Shape the Rolls: Roll the dough out to a 12×8 inch rectangle, about ½ inch thick. Cut the dough into even pieces using a sharp knife to create 24-30 pieces.
Second Rise: Transfer the rolls 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.
Bake the Rolls: About 20 minutes before the rolls are done rising, preheat the oven to 350°F (175°C). Bake the rolls for 12-15 minutes or until golden brown.
Finish and Serve: Remove the rolls from the oven and brush them with melted butter. Serve warm and enjoy!