Preparation

1. In a small saucepan, combine the milk, butter, and sugar. Warm over low heat until the butter is melted. Remove from the heat and reserve.
2. In a 2-cup measuring cup, dissolve the yeast in the warm water. Let stand until foamy, about 5 minutes.
3. Once the milk mixture is completely cool, stir in the egg. Put the flour and salt in a food processor work bowl fitted with the metal chopping/dough blade. Process to sift, about 15 seconds.
4. With the machine running, add the proofed yeast, then the cooled milk and egg mixture slowly through the feed tube. Process until a dough ball forms. Once a dough ball forms, continue processing for 45 seconds to knead the dough.
5. Shape the dough into a smooth ball and transfer to a large mixing bowl; cover with plastic wrap. Allow to rise in a warm place until doubled in size, 45 to 60 minutes.
6. While the dough is rising, preheat the pizza oven to 400°F with the baking stone in place. Lightly butter a 9-inch round baking pan.
7. Once the dough has risen, divide into 12 equal pieces (about 2 ounces each).
8. Roll each piece into a smooth round and arrange in the prepared pan. Cover with plastic wrap and allow to rise until doubled in size, 30 to 40 minutes.
9. Once ready to bake, brush the risen dough with the egg wash. Bake until golden brown and the internal temperature is 200°F, about 30 minutes.
10. Remove the rolls from the pan, and let cool on a rack for about 10 minutes before serving.