Adjust oven rack to middle position and preheat oven to 475 degrees.
Combine 1 tablespoon oil, garlic, red pepper flakes, and 1/2 teaspoon salt in a 12-inch oven-safe nonstick skillet and sauté over medium-high heat until fragrant, about 1 minute.
Add crushed tomatoes, water, ziti, and 1/2 teaspoon salt.
Cover and cook, stirring often and adjusting heat as needed to maintain vigorous simmer, until ziti is almost tender, 12 to 15 minutes. Make sure you don't cook it too much; it will continue to cook in the oven.
While the pasta is cooking, combine ricotta, remaining 1 teaspoon olive oil, 1/4 cup of grated Parmesan cheese, 1/4 teaspoon salt, and 1/8 teaspoon pepper in a bowl. Set aside.
Stir in heavy cream, 1/2 cup Parmesan, and basil into the pasta and season with salt and pepper to taste.
At this point, if your skillet is not oven-safe, transfer the pasta mixture into a shallow 2-quart casserole dish before sprinkling with the ricotta and cheese and baking. If you're really against turning on the oven, you could cover the skillet with a lid and melt the cheese that way, but it won't get browned and toasty.
Add dollops of the ricotta mixture with a spoon on top of the pasta and sprinkle mozzarella evenly over ziti.
Transfer skillet to oven and bake until cheese has melted and browned, about 5 to 10 minutes. Let cool slightly and sprinkle with remaining tablespoon of basil. Serve.
