In a small saucepan set over low heat, whisk together the whole milk, water and flour until smooth. Cook until the mixture thickens, about 3 to 5 minutes. Remove from the heat and set aside.
To Make the Dough
In the bowl of a stand mixer, combine the flour, dry milk, sugar, salt and yeast. Mix on low until combined. In a 2 cup glass measuring cup, warm the milk in the microwave. Whisk in the starter, eggs and melted butter. With mixing speed on low, gradually add the wet ingredients. Mix just until a dough forms. Switch to the dough hook and knead for 15-20 minutes.
Shape the dough into a ball and transfer to a lightly buttered bow. Cover with plastic wrap and place into a warm oven (I turn mine on to 200 degrees, then turn it OFF when it reaches that temperature) for 60 to 90 minutes or until doubled.
Gently deflate the dough by pressing a fist into the center. Divide into 12 equal pieces, and shape each piece into a ball. I like to pinch the bottom of the balls of dough and then form a C shape with my hand and roll the ball on the counter to make a smooth, taut circle. That way the rolls have a more uniform shape. If you have a kitchen scale, weighing them will help with that too.
Place the rolls into a lightly buttered quarter sheet pan or 9x13-inch pan. Cover with a clean towel and return to the oven. Let the rolls rise for 40 to 50 minutes, or until puffy.
Preheat oven to 350 degrees. In a small bowl whisk together the egg and milk. Brush the tops of the rolls and bake for 20 to 25 minutes, or until golden brown on top (a digital thermometer inserted into the center of the roll should reach 190 degrees +).
Remove the rolls from the oven and brush the tops with butter. Allow the rolls to cool for 10 minutes before pulling apart and serving.
Notes
-If you don't have a electric mixer, try kneading the dough for as long as you can stand. The dough can also be kneaded in a Bosch mixer or bread machine. -Freeze these rolls and let them thaw at room temperature for a few hours before warming.