Boil the pasta: Cook the rigatoni in salted boiling water for 2 minutes less than the package directions, so it stays firm at the center. Drain and set aside; it will finish cooking in the sauce later.

Brown the sausage: Heat the olive oil in a large skillet over medium-high heat. Add the beef sausage, breaking it into crumbles with a spoon, and cook until no pink remains, about 6 minutes.

Soften the vegetables: Add the onion and bell peppers to the skillet with the sausage. Cook, stirring occasionally, until the vegetables soften and the edges turn golden, about 5 minutes.

Add garlic and spice: Stir in the minced garlic and red pepper flakes. Cook just until fragrant, about 30 seconds, stirring constantly so the garlic doesn't burn.

Build the sauce: Pour in the crushed tomatoes, chicken broth, and balsamic vinegar, scraping up any browned bits from the bottom of the pan. Stir in the oregano, salt, and black pepper.

Simmer the sauce: Bring the sauce to a gentle simmer and cook uncovered for 10 minutes, stirring occasionally, until it thickens enough to coat the back of a spoon.

Add the pasta: Fold the undercooked rigatoni into the sauce. Simmer for another 3 to 4 minutes, stirring often, until the pasta is tender and coated evenly in sauce.

Finish and serve: Remove the skillet from the heat and sprinkle with parmesan cheese and torn fresh basil. Serve immediately straight from the skillet.