Add pasta and 1 tablespoon salt and cook, stirring occasionally, until just beginning to soften, about 5 minutes.
Reserve 1 1/2 cups cooking water, then drain pasta.
Rinse pasta with cold water and drain again, leaving pasta slightly wet, leave in colander.
Dry now-empty pot, add 1 tablespoon oil, and return to medium-high heat until shimmering.
Add sausage and cook, breaking up meat with wooden spoon, until no longer pink, about 5 minutes.
Stir in garlic and cook until fragrant, about 30 seconds.
Stir in crushed tomatoes and tomato sauce, bring to simmer, and cook until slightly thickened, about 5 minutes.
Let cool to room temperature, 30 to 45 minutes.
Stir reserved cooking water, pasta, mozzarella and basil into cooled sauce; transfer to 13 by 9-inch baking dish.
Combine ricotta, remaining 3 tablespoons oil, 1/2 teaspoon salt and 1/4 teaspoon pepper in bowl; cover.
Wrap dish tightly with plastic wrap and refrigerate ziti and ricotta separately for at least 8 hours or up to 24 hours.
Adjust oven rack to middle position and heat oven to 400°F.
Unwrap dish and cover tightly with greased aluminum foil.
Bake casserole until beginning to bubble around edges, about 20 minutes.
Remove foil and dollop rounded tablespoons of ricotta mixture evenly over top.
Sprinkle with mozzarella and Parmesan and bake, uncovered, until casserole is hot throughout and cheese is melted and begins to brown, 15 to 20 minutes.
Let cool for 10 minutes. Sprinkle with basil and serve.
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