To make the dough in a food processor: In a food processor, combine both flours; pulse a few times to combine. With the machine running, slowly add ¾ cup water through the feed tube. Process until the dough forms pea-sized clumps, about 25 seconds. If the dough is too sandy and dry to form clumps, pulse in more water, a few drops at a time; if the dough feels sticky, add more all-purpose flour or semolina, a sprinkle at a time.

To make the dough by hand: In a large bowl, whisk together both flours. Make a well in the center, then add ¾ cup water. Using a fork, stir in a circular motion, starting in the center and gradually moving outward to incorporate the water and flour mixture, until a shaggy dough forms. Using your hands, bring the dough together and knead, swiping along the edges of the bowl to incorporate any dry bits. If the dough resists coming together, add more water, a few drops at a time; if the dough feels sticky, add more all-purpose flour or semolina, a sprinkle at a time. The dough should be moist enough to form a cohesive mass without sticking to the sides of the bowl; it’s fine if it’s a little crumbly.

Lightly dust the counter with semolina and turn the dough out onto it. Knead until soft, smooth and springy, about 10 minutes. Form into a ball, cover with plastic wrap and let rest at room temperature for at least 20 minutes or for up to 1 hour. Alternatively, wrap tightly in plastic wrap and refrigerate up to 2 days; if refrigerated, let the dough stand at room temperature for 1 hour before proceeding.

Lightly dust 2 rimmed baking sheets with semolina. Unwrap the dough and cut it into quarters. Set 3 pieces aside and cover lightly with plastic wrap. Using your palms, roll the remaining piece into a log. Lightly dust the counter with semolina, then roll the log to form a rope about ½ inch in diameter; if the rope’s length becomes difficult to manage, cut it in half, then roll the pieces separately.

Cut the rope into ¼-inch pieces and lightly dust with semolina. On an unfloured area of the counter, set 1 piece cut side up. Press the flat of your thumb into the center of the piece and, while applying light pressure, smear or drag the dough against the counter with slight twisting action; the dough may curl a bit around your thumb. The finished shape should resemble a shallow cup that is thinner at the center and thicker at the perimeter. Set the orecchiette on a prepared baking sheet. Shape the remaining dough pieces in the same way; try to keep the orecchiette separated on the baking sheet to avoid sticking. Repeat with remaining dough. If not cooking right away, let stand uncovered at room temperature up to 4 hours.

To cook the orecchiette, follow the directions in the pasta recipe you are making, or in a large pot, bring 4 quarts water to a boil. Add 1 tablespoon salt and the orecchiette, then cook, stirring occasionally, until al dente. Reserve some of the cooking water if directed in your recipe, then drain the pasta.

Homemade Cavatelli: Follow the recipe to make the dough and portion the first piece into ¼-inch pieces. Dust a gnocchi board with semolina or have ready a dinner fork. Holding the board or fork, with the backside of the tines facing up, at an angle, press a piece of dough into the board or fork tines with the side of your thumb and swipe downward; the dough will curl, creating a U shape with ridges on the outer side. Transfer to a prepared baking sheet and repeat with remaining dough.

Hand-Rolled Thick Spaghetti (Pici): Follow the recipe to make and rest the dough, then cut it in half. Flatten both pieces into disks; cover one lightly with plastic wrap. Dust the counter with semolina and set the second disk on top. Using a rolling pin dusted with semolina, roll the disk to an even ⅛-inch thickness. Using a chef’s knife and a decisive cutting motion (do not use a sawing action), slice the dough into ¼-inch thick strips. Lightly dust the counter with semolina, then using your fingertips, gently roll the dough back and forth against the counter into long, thin noodles about ⅛ inch in thickness. Transfer to a prepared baking sheet, keeping the noodles separate to avoid sticking. Repeat with remaining dough.