Add 3 cups of flour, yeast, sugar, salt in the bowl of a stand mixer. Stir together. Add warm milk, softened butter, and egg.
Attach the dough hook and turn the mixer on to the lowest speed, mix until flour is incorporated, scraping down the sides of the bowl as necessary.
Increase speed to medium and beat for 2 minutes.
Add ½ cup flour and blend with the dough hook until incorporated. And another ½ cup flour and repeat, mixing at medium speed for another 1-2 minutes until a ball of dough is formed. Add up to ½ of additional flour until the dough ball is slightly sticky and pulling away from the sides of the bowl.
Transfer the dough to a lightly greased bowl and cover with a towel and let rise for 30 minutes at room temperature.
Remove the towel and deflate the dough by punching down lightly.
Pinch off pieces of the dough to form 20 equally sized dough balls.
Transfer the rolls to a lightly greased 9x13 baking dish. Cover with a towel and let rise for an additional 30 minutes at room temperature.
Preheat the oven to 375°F. Bake the rolls for 15-17 minutes or until golden brown and cooked through. If the rolls are getting too brown, just tent the rolls with foil.
Remove rolls and brush hot rolls with the melted butter. Serve immediately or store cooled rolls in a plastic bag for up to 3 days.