Set the pasta dough aside covered with a damp towel for about 30 minutes. In a medium bowl, combine the ricotta, egg, parsley, Parmesan, ham, mozzarella, salt and pepper, and stir to thoroughly combine. Roll out the pasta dough into a 1/8-inch thick sheet and place mounds of about 2 tablespoons of the filling equally spaced along half of the dough. Fold the dough over to cover the mounds, and cut around each mound of filling using a 3-inch cookie cutter, press the edges firmly to seal and pressing to release as much of the trapped air as possible. Crimp the edges, if desired. Place the ravioli on a baking sheet or large plate, covered with plastic wrap or a lightly damp towel, and refrigerate until ready to serve, up to overnight.
Fill a large pot with water and add salt to taste. Bring to a boil. Add the ravioli and cook until they float to the surface, about 3 minutes. Drain briefly on paper towels, then transfer to shallow bowls and serve, with a heaping 1/4 cup of the warmed tomato sauce spooned over the top and garnished with chopped basil and Parmesan.
Place all the ingredients in the bowl of a food processor and pulse until a ball is formed. Continue to pulse for 1 minute and remove from the processor. Continue to knead by hand for 5 minutes before forming into a tight ball and covering with a damp towel.