Put 2 1/2 cups of the flour into a bowl and toss with the salt. Make a well in the flour, and add the cheese and eggs. Gradually work the mixture together, adding more flour if necessary, to make a soft but not sticky dough. The gluten free flour likely will not need more than the 2 1/2 cups.
On a lightly floured surface, knead the dough until it is smooth. Let the dough rest at room temperature in a bowl covered with plastic wrap, for 30 minutes.
Form the dough into a round and cut into quarters. Working with one quarter at a time (cover the remaining dough in the bowl with plastic wrap), on a lightly floured surface, roll the dough into a rope, around 1/4-inch to 1/2-inch in diameter.
With a knife, cut the rope into 1/2-inch to 1-inch pieces, depending on the size pasta you prefer. With your index and middle fingers held together, gently press down on each piece, beginning at the top and moving down toward the bottom, dragging your fingers toward you and causing the pasta to roll over on itself.
Transfer the formed pasta to a lightly floured jelly-roll pan and let dry at room temperature for at least 30 minutes. Meanwhile, bring a saucepan of water to a boil.
Salt the water, and add the pasta. Cook until the cavatelli are al dente. They are done when they float to the top, about 3 to 4 minutes. Drain the cavatelli, then use them them for Baked Ricotta Cavatelli with Mascarpone Cheese Sauce, or add your favorite sauce and serve. Alternatively, freeze them for later use.