Cook rigatoni according to package directions; reserve 1/2 cup pasta water and drain.
Season chicken with salt, pepper, and Italian seasoning. Sear in olive oil over medium-high heat until cooked through; remove and set aside.
Sauté onion until translucent, add garlic and cook 30 seconds. Add chopped roasted peppers and chicken broth; simmer 3 minutes.
Blend pepper mixture until smooth (use an immersion blender or regular blender). Return to pan, stir in cream and Parmesan until sauce thickens.
Add chicken, pasta, and a splash of reserved pasta water to loosen sauce. Toss with basil, adjust seasoning, and serve with extra Parmesan.