In a 1-quart saucepan, heat the milk and 1/4 cup butter over medium-low heat, stirring frequently, until very warm and an instant-read thermometer reads 120°F to 130°F. Add the milk mixture and the egg to the flour mixture. Beat with an electric mixer on low speed 1 minute, stopping frequently to scrape batter from side and bottom of bowl with a rubber spatula, until flour mixture is moistened. Beat on medium speed 3 minutes, stopping frequently to scrape bowl. With a wooden spoon, stir in enough of the remaining flour, 1 cup at a time, until dough is soft, leaves side of bowl and is easy to handle (dough may be slightly sticky).