Preheat the oven to 450 degrees F. Bring a large pot of salted water to a boil.
Heat the oil in a medium saucepan over medium heat. Add the garlic and red pepper flakes and cook, stirring, until the garlic is golden, about 2 minutes. Add both cans of the tomatoes and 1 cup of water. Increase the heat to medium-high and bring to a simmer. Reduce the heat slightly, add the basil sprig and simmer rapidly, uncovered, until thickened, 15 to 20 minutes. Discard the basil and stir in the ricotta. Season with salt and pepper.
Cook the ziti in the water until very al dente, about 2 minutes less than the package directions specifies. Drain the pasta and transfer it to a large bowl.
Add the tomato sauce, the chopped basil, artichokes, peppers, olives, the mozzarella and half of the Parmesan to the bowl and stir well to combine. Transfer the pasta to a 3- to 4-quart baking dish and top with the provolone and the remaining Parmesan. Bake, uncovered, until browned, about 15 minutes. Let the pasta rest for about 10 minutes before serving.
Copyright 2016 Television Food Network, G.P. All rights reserved.