Boil rigatoni until al dente, then drain and set aside.
Heat oil in a skillet, sauté chicken with salt and pepper until cooked through.
Add onions, garlic, Cubanelle peppers; cook until softened.
Stir in crushed tomatoes, roasted red peppers, and hot cherry peppers.
Simmer sauce for 10 minutes, then add cream and Parmesan.
Fold in cooked pasta, toss to coat evenly.
Simmer for another 5 minutes to marry the flavors.
Serve hot with extra Parmesan or fresh herbs if desired.