Step 1

In a large bowl, combine the flour and yeast, stirring to blend.

Step 2

In a medium saucepan over low heat, add the milk and butter. Stir frequently, until the butter melts. Add the sugar and salt and stir until they dissolve. Remove from the heat and let cool to room temperature.

Step 3

Pour the cooled milk mixture into the bowl of a stand mixer fitted with the dough hook. Add the flour mixture, water, potatoes, and eggs and mix on low speed for 3 minutes. Increase the speed to medium and mix until you have a smooth dough, about 7 minutes more.

Step 4

Transfer the dough to a lightly floured surface. Sprinkle the top of the dough with flour and do a final kneading of the dough, shaping it into a ball and tucking the edges of the dough to the bottom center, creating a smooth, taut ball.

Step 5

Lightly spray a large bowl with nonstick spray. Add the dough and turn to coat with oil, then turn seam side down, cover with a tea towel or plastic wrap, and let rise in a warm, draft-free place until doubled in size, 1 to 1 1/2 hours.

Step 6

Lightly butter a 12- by 17-inch (30- by 43-cm) rimmed baking sheet. Alternatively, you can use two 9- by 13-inch (23- by 33-cm) baking pans.

Step 7

Turn the dough out onto a lightly floured surface and divide into 48 (about 1 1/2-ounce or 44 g) pieces. Shape into balls and place in the prepared pan, 8 rows by 6, arranging them on the baking pan so they just barely kiss each other. (You also have the option to cover and refrigerate the rolls in the pan until ready to bake, up to 1 day.)

Step 8

Allow the rolls to rise in a warm, draft-free place until doubled in size, 1 to 1 1/2 hours. (If your rolls were refrigerated overnight, this may take 2 to 3 hours.)

Step 9

When you are ready to bake, preheat the oven to 400°F (205°C).

Step 10

In a small bowl, beat the egg yolk and cream together. Lightly brush the tops of the rolls with the egg wash.

Step 11

Bake the rolls until golden brown, 16 to 24 minutes. Remove from the oven and serve warm with butter alongside, if desired.