Bring a large pot of water to a boil. Add the salt and orecchiette and cook until done, about 8 minutes for freshly made or about 20 minutes for dried.

Meanwhile, combine the tomatoes, garlic, and olive oil in a large bowl. Season with salt and pepper, but keep in mind that the cheese will add more saltiness. (This sauce can be kept at room temperature for several hours and will get more garlicky as it sits.) When the pasta is cooked, drain it and toss it with the tomato mixture. Sprinkle with the basil and cheese and serve immediately.

In a bowl, whisk the flours together well. Mound the flour on a work surface, make a deep well in the center, and pour 2 tablespoons of the water in the center. With two fingers, stir in a little flour from the walls of the well. When the water is absorbed and a paste has formed, repeat with more water until you have a soft but not sticky dough.

Knead the dough on a lightly floured surface until it's smooth and supple, 7 to 8 minutes. If it crumbles during kneading, wet your hands to moisten the dough slightly. Cut off a golfball-size chunk of dough; cover the rest with plastic wrap. Roll the chunk into a cylinder about 1 inch in diameter. With a very sharp knife, slice the cylinder into disks about 1/8 inch thick.

Pick up a disk. If it's squashed from cutting, squeeze it slightly between your thumb and index finger to return it to a circular shape. Put the disk in the palm of one hand and press down on it with the thumb of your other hand. Swivel your hand (not your thumb) twice to thin the center of the ear, leaving the rim a little thicker. If the dough sticks to your thumb, dip your thumb in a little flour as you work. Repeat with the rest of the dough. As you finish the disks, lay them on a clean dishtowel. When you've shaped an entire cylinder, sprinkle a little flour over the ears and repeat the process with a new chunk of dough.

If you're not cooking the pasta immediately, spread the rounds out on floured baking sheets and leave them at room temperature at least overnight, or until they're hard enough that you can't slice them with a knife. (The time they take to dry depends on humidity and the moisture level in the dough itself.) Once the orecchiette are dry, transfer them to covered jars and store at room temperature.

Make Ahead: Dried orecchiette can be stored in airtight containers for up to two months.