Step 1In a small pan, heat one-half cup plus 2 tablespoons of milk over medium heat, just until warmed. Remove from heat, and pour the milk into a small bowl or measuring cup. Stir in the yeast and 1 teaspoon of sugar, then set aside until the milk is foamy and the yeast is activated, about 10 minutes.
Step 2Whisk 2 eggs in the bowl of a stand mixer using the whisk attachment (or in a large bowl with a hand mixer) until light and fluffy, about 1 minute. Stir in the yeast mixture and remaining 1/4 cup of sugar until fully incorporated.
Step 3If using a stand mixer, switch to the paddle attachment. With the mixer running, add the butter, 1 tablespoon at a time, until incorporated.
Step 4In a medium bowl, whisk together the flour and salt. With the mixer running, add the flour mixture, one spoonful at a time, until fully incorporated.
Step 5Remove the dough to a lightly floured surface and knead until it is soft and somewhat silky (it's a rich dough and won't be entirely smooth), 5 to 7 minutes. Place the dough in a large oiled bowl and lightly cover with plastic wrap. Set aside in a warm place until doubled in size, 1 to 1 1/2 hours. (Alternatively, you can refrigerate the dough overnight, then take it out the next day and wait for it to come to room temperature.)
Step 6Meanwhile, make an egg wash: Beat together the remaining egg with the remaining 2 tablespoons of milk.
Step 7Heat the oven to 375 degrees. Line a baking sheet with parchment paper and lightly grease the parchment.
Step 8When the dough is doubled (it will be very smooth and elastic), punch it down and divide it into 6 pieces, each weighing about 5 ounces. Form each piece into a ball, pinching the seams together at the base of each one. Flatten the ball so it’s about 1 inch thick and place on the prepared baking sheet; continue until you have six rounds evenly spaced on the sheet.
Step 9Lightly brush each round with the prepared wash (for deeper coloring, brush the rounds a second time after the first wash has dried), and set aside until the rounds are puffed and almost doubled in size, about 15 minutes.
Step 10Bake the rounds until they are puffed and a rich golden color, about 20 minutes, rotating halfway for even coloring. Cool completely on a rack before slicing and serving.