In the bowl of a heavy-duty stand mixer, combine the 3¾ 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 Parmesan 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. 12-15 minutes, adding more flour if too sticky. Transfer the dough to a floured work surface and knead by hand for 1-2 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 volume, 1 to 1½ hours.

Position a rack in the lower part of an oven and preheat the oven to 425°F. Brush a 9-inch round pan with olive oil. Place the remaining 1/4 cup Parmesan 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 to form the dough into a log about 12 inches long. Cut the log in half crosswise, then cut each half crosswise into 6 equal pieces. Knead each dough piece a couple of times, roll it between the palms of your hands into a ball, and then roll it in the cheese to coat lightly and evenly, shaking off any excess. As each ball is coated, place it in the prepared pan, resting it against the rim and pressing down slightly to form a 2-inch disk. Arrange 9 balls around the rim and 3 balls in the center. Cover loosely with plastic wrap and let rise again in a warm place until doubled in size, 30 minutes. Sprinkle the top with the cheese remaining on the plate. Using a razor blade or sharp knife, cut a slash 1/4 inch deep in the top of each ball. Bake for 10 minutes. Reduce the oven temperature to 375°F and continue baking until brown and crusty, 20-30 minutes longer.

Transfer to a wire rack and let rest in the pan for 1-2 minutes, then remove from the pan; the rolls will come out in a single loaf. Serve the loaf warm, breaking off the rolls at the table. Or let cool, top side up, on the rack.