Bring a large pot of water to a rolling boil. Add 2 tablespoons kosher salt - it should taste like the sea. Add rigatoni and cook 2 minutes less than package directions for al dente (usually about 10 minutes). The pasta will finish cooking in the oven. Drain well, do not rinse, and set aside.

Heat a large oven-safe skillet or Dutch oven over medium-high heat. Add the sausage, breaking it into walnut-sized chunks with a wooden spoon. Cook without stirring for 3 minutes to develop a crust, then continue cooking and breaking apart until browned and cooked through, about 6 minutes total. Transfer to a plate with a slotted spoon, leaving the rendered fat behind.

Reduce heat to medium. Add onion to the fat in the pan and cook, scraping up any browned bits, until softened and translucent at the edges, about 5 minutes. Add garlic and red pepper flakes (if using) and cook until fragrant, 30 seconds to 1 minute - do not let the garlic brown.

Add crushed tomatoes, oregano, and half the torn basil. Season with 1 teaspoon salt and several grinds of black pepper. Return sausage to the pan, stir to combine, and bring to a gentle simmer. Cook uncovered for 10 minutes, stirring occasionally, until slightly thickened. Taste and adjust seasoning.

Preheat oven to 400 degrees F. Add the drained rigatoni to the sauce and toss until every tube is coated. If your skillet isn't oven-safe, transfer to a 9x13 inch baking dish now.

Dollop ricotta evenly over the surface, then use the back of a spoon to nestle some of it down into the pasta. Scatter shredded mozzarella and half the Parmigiano over top. Drizzle with olive oil.

Bake uncovered until the cheese is melted, spotty brown, and the edges are bubbling vigorously, 20 to 25 minutes. Let rest 10 minutes before serving - this sets the cheese and prevents mouth burns. Scatter remaining basil and Parmigiano over top.