In a stand mixer, combine 3 cups of flour, yeast, sugar, salt, warm milk, butter and egg.
Using a dough hook or paddle attachment, mix the ingredients until combined on low speed, scraping down the sides often.
Continue to add 1/4 cup of flour at a time mixing on medium speed, until the dough doesn't stick to the sides of the bowl and clings to the dough hook. Mix for 3-5 minutes. When the dough is ready, it will feel smooth and it will come off your fingers if you pinch it.
Lightly grease a large bowl or you can use the same mixing bowl with nonstick cooking spray or oil. Form the dough into a ball shape making sure to coat it evenly in the oil. Cover the bowl with a warm damp towl and let the dough rise in a cool-warm environment for 30-40 minutes, until it has doubled in size. (I place my dough to rise on the kitchen counter)
Once the dough has risen, punch the dough ball down to release the air. Grease a 9 x 13 inch baking pan and divide the dough to form 24 rolls by shaping each roll into a smooth round ball. Place the rolls onto the greased baking pan, cover and let rise again for 30 minutes in a cool-warm environment. They will be a bit puffy. Preheat oven to 375 degrees F towards the end of the rising time.
Bake the rolls for 12-15 minutes, or until the tops of the rolls turn golden brown. Remove rolls from the oven and brush melted butter onto the tops of each roll before serving. Enjoy!