Heat a large pot over medium-high heat. Cook and stir sausage and ground beef in the hot skillet until browned and crumbly, 5 to 7 minutes. Add tomato sauce, whole tomatoes with juice, onion, garlic, Italian seasoning, basil, sugar, and red pepper flakes; bring to a simmer. Reduce heat to medium-low and simmer for 30 minutes to 1 hour. Turn off the heat. Transfer 3 cups sauce to a bowl and leave remaining sauce in the pot; allow to cool while you prepare ziti.

Preheat the oven to 375 degrees F (190 degrees C).

Bring a large pot of lightly salted water to a boil. Add ziti and cook, stirring occasionally, until tender yet firm to the bite, about 11 minutes. Drain ziti and rinse under cool water to stop it from cooking.

Combine ricotta, 2 cups mozzarella, Parmesan, egg, 2 tablespoons parsley, and pepper in a bowl; stir together with a few turns but do not mix completely. Pour drained ziti into the bowl and toss until slightly combined with large lumps. Add the reserved 3 cups meat sauce and toss to combine.

Place 1/2 of the pasta mixture into a 9x13-inch casserole dish. Spoon 1/2 of the remaining sauce over top, layer with 6 slices of provolone and 1 cup mozzarella. Repeat layers: pasta mixture, remaining sauce, 6 slices provolone, and 1 cup mozzarella. Cover with foil.