1Make the starter: on a pan over medium heat, add 3 tablespoons of water, 3 tablespoons of whole milk, and 2 tablespoons of bread flour.
2Mix the ingredients together until it forms a paste that looks like mashed potatoes.
3Put the starter off to the side and let it cool down.
4In a mixing bowl, add 2 1/2 cups of bread flour, 1/3 cup of melted butter, 1/2 cup of whole milk, 4 tablespoons of sugar, 1 tablespoon of yeast, 2 tablespoons of dry milk powder, 1 teaspoon of salt, and 1 egg.
5Add the cooled-down starter to the mixing bowl.
6Mix the dough for 10 minutes on medium speed using a stand mixer.
7Put the dough into a lightly greased bowl, twirl it around, and cover it with plastic wrap.
8Let the dough prove for about 1 to 1.5 hours, or until it doubles in size.
9Punch down the dough to release the air.
10Divide the dough into 6 equal pieces.
11Roll each piece of dough into a ball by pinching and forming a ball with your hand, then gliding it with the palm of your hand, thumb, and pointer finger to create a perfect little ball.
12Place the dough balls into a greased pan.
13Wrap the pan with plastic wrap again and let them prove for another 30 minutes.
14Brush the rolls with egg wash.
15Bake in the oven at 350°F (175°C) for 25 minutes.