Brown sausage in a 6-quart Dutch oven over medium-high heat for 7 minutes, breaking it into crumbles and cooking it to 160°F. Drain excess fat, leaving about 1 tablespoon.
Add peppers and onion and cook for 7 minutes until softened at the edges. Stir in garlic and oregano for 30 seconds.
Add tomato sauce, broth, salt and pepper and bring to a boil. Stir in rigatoni and reduce to a steady uncovered simmer.
Cook for 13 to 16 minutes, stirring from the bottom every 2 minutes and adding reserved water in small amounts if the pot becomes dry before the pasta is tender.
Remove from the heat and stir in Parmesan. Rest for 3 minutes and divide among 5 bowls.