3 3/4 cups unbleached bread flour, plus more as needed
1 pkg active dry yeast
2 tsp salt
1 1/3 cups warm water
1/2 cup freshly grated Parmigiano-Reggiano cheese
Olive oil, for brushing
1 egg yolk
In the bowl of a heavy-duty stand mixer, combine the 3 3/4 cups flour, the yeast and salt. Add the warm water and stir with a wooden spoon until just mixed together. Sprinkle 1/4 cup of the cheese over the dough. Fit the mixer with the dough hook and begin mixing and kneading on very low speed. When the mixture pulls away from the sides of the bowl, increase the mixer speed to medium-low and continue to knead until the dough is smooth and elastic, 12 to 15 minutes, adding more flour if the dough is too sticky. Transfer the dough to a floured work surface and knead by hand for 1 to 2 minutes.
Form the dough into a ball, brush it with a little olive oil and return it to the bowl. Cover with a towel and let rest in a warm, draft-free place until doubled in bulk, 1 to 1 1/2 hours.
Brush a 9-inch round pan with olive oil. Place the remaining 1/4 cup cheese on a plate. Punch down the dough. Return it to the floured work surface and knead a few times. Then, using your palms, roll the dough to form a log about 12 inches long. Cut the log in half crosswise, then cut each half into 6 pieces (I made rolls the size of golf balls for sliders and got approximately 20). Fold the dough under into into a ball, roll it in the cheese to coat lightly and evenly, shaking off any excess. As each ball is coated, place it on a greased cookie sheet and press down slightly to form a 2-inch disk. Cover loosely with plastic wrap and let rise again in a warm place until doubled in bulk, 30 to 40 minutes.
Position a rack in the lower third of an oven and preheat to 425°F.
Beat the egg yolk with a tablespoon of water and brush the tops of the rolls. Sprinkle the top with the cheese remaining on the plate. Using a razor blade or sharp knife, cut a shallow slash in the top of each ball. Bake for 5 minutes. Reduce the oven temperature to 375°F and continue baking until brown and crusty, 10 minutes more. Transfer the pan to a wire rack and let the rolls rest in the pan for 1 to 2 minutes, then remove them from the pan.
by William Sonoma