Preparation

1. In a small saucepan, combine the milk, butter and sugar. Warm over low heat until the butter is melted. Remove from 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. Put the flour and salt into the large work bowl fitted with the dough blade. Process on Low to sift, 10 seconds. Add the milk mixture and egg to the yeast mixture. Gently stir to combine.
4. With the machine running on Low, slowly add the liquid through the feed tube and process until a dough ball forms. Continue processing to knead the dough, 45 seconds. 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, about 45 to 60 minutes.
5. Preheat oven to 450°F. Lightly butter a 9-inch round baking pan. Divide the dough into 12 equal pieces, about 2 ounces each. Roll into smooth rounds and arrange in the prepared pan. Cover with plastic wrap and allow to rise until the rolls have doubled in size, about 30 to 40 minutes.
6. Just before baking, gently brush the rolls with the egg wash. Bake until golden brown or an internal temperature of 200°F is reached, about 12 to 15 minutes.
7. Remove rolls from pan and cool on a rack for about 10 minutes before serving. For a softer roll, brush each with melted butter just after removing from the oven.