Step 1

In a small microwave-safe bowl combine the milk and water. Heat until lukewarm, 20 to 30 seconds on high heat. (This can also be done in a small saucepan on the stove.)

Step 2

In the bowl of an electric mixer fitted with the dough hook, combine the egg, flour, potato flakes, dried milk, sugar, yeast, salt, and 3 tablespoons of the butter. Add the warm milk and water mixture and knead on medium-low speed for about 5 minutes until you have a smooth, soft dough. (Don’t worry if the dough sticks a bit to the bottom of the bowl.) To remove the dough from the bowl, dust your hands with flour and scrape it out.

Step 3

Using your hands (dust them with more flour if necessary), shape the dough into a ball and place in a lightly greased bowl. Cover the bowl with plastic wrap or a damp kitchen towel and let the dough rise in a warm, draft-free place until it's doubled in bulk, about 90 minutes.

Step 4

Invert the dough onto a lightly floured work surface (it will deflate). Divide it into 12 even pieces (each piece should weigh 1¾ to 2 ounces). Shape each piece of dough into a smooth ball by tucking and pinching the edges underneath to form a plump little bun.

Step 5

Grease a 9-inch round baking pan with nonstick cooking spray. Place the rolls in the pan, arranging 8 evenly around the perimeter and 4 in the center. Cover the pan with plastic wrap or a damp kitchen towel and let the rolls rise until they're almost doubled in bulk, puffy, and touching, about 1 hour. Toward the end of the rising time, preheat the oven to 350°F and set an oven rack in the middle position.

Step 6

Melt the remaining 1 tablespoon butter. Brush the rolls with the melted butter and bake for 23 to 25 minutes, until golden brown. Remove from the oven, and turn out onto a wire rack. Serve warm or at room temperature with butter. Store the rolls in a sealable plastic bag for several days at room temperature, or freeze for longer storage.