Preheat oven to 425°F. On a rimmed baking sheet, toss red onion wedges with 1 tablespoon olive oil and 1/4 teaspoon each salt and pepper. Roast for 15 to 20 minutes, until golden brown and tender.
Meanwhile, cook rigatoni according to package directions. Reserve 1/2 cup pasta cooking water, then drain.
In a large bowl, toss hot pasta with 1/4 cup reserved pasta water and Pecorino Romano. Add more pasta water if needed to loosen.
Fold in roasted onions, marinated peppers, and season with salt and pepper to taste.
Toss with torn basil leaves and drizzle with additional olive oil. Serve topped with more grated Pecorino, if desired.