1 Mix the dough: In the bowl of a stand mixer on low speed with the paddle attachment, stir 2 cups of the flour, the potato flakes, yeast, sugar, and salt until combined. Add the eggs and milk and beat for 1 minute at medium speed.
Add the butter in tablespoon size pieces on medium speed and beat until it is incorporated. This will take about 3 to 5 minutes. Scrape down the sides of the bowl and mix in 1 1/2 cups more flour at low speed. The dough will be thick and smooth.
Scrape down the sides of the bowl again and switch to the dough hook. Set the mixer on low speed and gradually add 1/2 cup more flour.
2 Knead the dough: Continue kneading the dough on low speed for 10 minutes or until it cleans the sides of the bowl. The dough should be soft and slightly tacky, but not so sticky that it will be difficult to shape into rolls.
If it is very sticky, add more flour, 1 tablespoon at time, until the dough pulls away from the sides of the bowl.
3 Let the dough rise: Turn the dough out of the bowl and form into a ball. Drizzle the oil into the bottom of the bowl. Set the ball back in the bowl and turn it to coat it with oil.
Cover the bowl with plastic wrap. Leave in a warm place to rise for 1 1/2 to 2 hours, or until doubled in size and the dough is firm but fingertips leave an impression in the dough.
4 Shape the rolls: Turn the dough onto a lightly floured countertop and, using a rolling pin, roll it into a 12-inch square that is even in thickness. This ensures that your rolls will be approximately all the same size. With a chef’s knife or pizza cutter, cut the square into 16 equal pieces of dough.
For each piece of dough, fold the edges into the center and pinch the loose ends together to form a ball. Turn the dough over so the seam side is down.
Move it to an unfloured part of your work surface (in order to take advantage of the traction of the board to shape the rolls). Cup your hands over the dough and rotate the roll, using your cupped fingers and your palm to make a round, taut roll.
5 Let the rolls rise: Line a rimmed baking sheet with parchment. Set the rolls on the sheet about 1-inch apart and cover with plastic wrap. Let the rolls rise for 1 hour, or until they have risen and look puffy. Toward the end of rising time, preheat the oven to 350°F.
Note: For rolls that “kiss” each other, set 4 in a row on the baking sheet. For separate rolls, spread them slightly farther apart.
6 Bake the rolls: Bake for 20 minutes, or until golden brown. Lift them off the baking sheet and set them on a rack to cool. If serving immediately, brush with melted butter (optional), or freeze (without the butter) and reheat at your convenience.
7 Freeze the rolls: In packages of 6 or 8, wrap the completely cooled, baked rolls tightly in foil. Slip the foil packages into plastic freezer bags and freeze for up to one month. (The rolls may develop frost and freezer burn after one month.)
Note: A one-gallon freezer bag conveniently holds a 6-pack of rolls, while a two-gallon bag will hold 2 8-packs.
8 Reheat the rolls: Remove the foil packages from the freezer bags and open the packages to allow air to circulate. Place them on a baking sheet in their open foil packets and heat in a 300ºF oven for about 10 minutes. If you like, brush with melted butter.