Preheat oven to 375°. In a medium saucepan over high heat, heat oil. Add sausage and break up with the back of a spoon into small pieces. Cook, stirring frequently, until cooked through and golden brown, 10 to 15 minutes. Transfer to a plate, leaving fat in skillet.

Return saucepan to medium-high heat. Cook onion, stirring occasionally, until slightly softened and lightly golden, 4 to 5 minutes. Add 3 cloves garlic and cook, stirring, until fragrant, about 1 minute; season with 1 teaspoon salt. Add crushed tomatoes and tomato puree and cook, stirring occasionally, until sauce is thickened, 25 to 30 minutes.

Meanwhile, in a large pot of boiling salted water, cook ziti until al dente according to package directions. Drain and transfer to a large bowl.

In a medium bowl, combine ricotta, pepper, ½ cup Parmesan, 1 ½ teaspoons salt, and remaining 1 clove garlic.

Remove sauce from heat. Stir in sausage, butter, and basil; season with remaining 1 ½ teaspoons salt. Add sauce and remaining ½ cup Parmesan to bowl with pasta and toss to combine.

Layer half of pasta mixture in a 15"-by-10" baking dish. Dollop with half of ricotta mixture. Sprinkle with ¼ cup Parmesan. Top with remaining pasta mixture, then dollop with remaining ricotta mixture. Sprinkle with mozzarella and remaining ¼ cup Parmesan.

Bake ziti until cheese is melted and lightly golden brown and sauce is bubbling around the edges, 40 to 45 minutes.