For the cavatelli: Add the flour to a large bowl and set aside. In a medium bowl, stir together the ricotta, eggs and 1/2 teaspoon salt. Stir the ricotta mixture into the flour.
Transfer the mixture to a floured work surface and, using your hands, gently bring the ingredients together to form a dough. Knead the dough together, adding additional flour as necessary, until the dough is firm and not sticky. Tightly wrap the dough with plastic wrap and allow to rest in the refrigerator for at least 1 hour and up to overnight.
On a lightly floured surface, cut the dough into 6 pieces, then roll the pieces into ropes about 1/4 inch in diameter. Cut the ropes into 1/2-inch pieces. Using your thumb or the dull side of a butter knife, press on each piece of dough and pull across the length of it. Continue until all the pasta dough is used. Transfer the pieces to a baking sheet dusted with semolina.
For the sauce: Warm the tomato sauce with the pulled chicken in a saucepan over medium heat.
Bring a large pot of water to a boil and salt liberally. Drop in the cavatelli, give them a gentle stir and boil until they begin to float, 3 to 4 minutes.
Transfer the cavatelli to the sauce along with 3/4 cup of the pasta cooking water. Stir until the pasta is thoroughly combined with the sauce. Remove from the heat and stir in the Parmesan, butter and basil, Serve with olive oil and cracked black pepper.
For more ingredient substitution ideas, see the article below.