Step 1 In the bowl of a stand mixer fitted with the paddle attachment, combine 1 cup of the flour, the yeast and the sugar. With the mixer on low speed, add the heated milk, mixing to combine, then add the butter. Continue to mix over medium speed for 2 to 3 minutes to begin to develop the dough. Add the egg and beat for an additional minute to combine.
Step 2 Switch to the dough hook, scraping down the bowl to make sure all of the ingredients are incorporated. Over low speed, gradually add the remaining flour, one spoonful at a time. Continue to mix for several minutes to develop the dough -- it will be smooth and elastic, and should clean the sides of the bowl.
Step 3Transfer the dough to a lightly oiled bowl, turning it in the bowl to oil the top of the dough. Cover and set aside in a warm place until doubled in size, about 1 hour.
Step 4Punch down the dough and turn out onto a lightly floured surface. Divide the dough into 6 even pieces (each slightly more than 4 ounces). Shape each piece into a ball, gathering the seams at the bottom of the ball and pinching them together to form a smooth round. Place the balls on a parchment-lined baking sheet, evenly spaced. Gently flatten each ball with the palm of your hand to form a disk about 4 inches in diameter. (If the dough springs back, leave it alone for a minute or so while you flatten the other balls to give it a chance to relax.)
Step 5Cover the mounds loosely with plastic wrap and set aside until puffed and nearly doubled in height, about 45 minutes. Meanwhile, heat the oven to 375 degrees.
Step 6Bake the buns until puffed and set, and golden brown on top, 15 to 18 minutes. Remove the buns from the oven and cool on the baking sheet for a couple of minutes, then transfer the buns to a cooling rack to cool completely. The buns can be stored in an airtight container for 3 to 4 days. Use a serrated knife to halve horizontally before using.