Heat olive oil in a large skillet over medium-high heat. Add the sausage and break it into bite-sized pieces with a wooden spoon. Cook for 6-7 minutes until browned and slightly crisp at the edges, stirring occasionally to prevent sticking.

Push sausage to the sides of the skillet, add diced onion to the center, and cook for 3 minutes until translucent. Stir in garlic and red pepper flakes, cooking for 30 seconds until fragrant.

Pour in crushed tomatoes, chicken broth, and tomato paste. Stir to combine, scraping up any browned bits stuck to the bottom of the pan. Bring to a simmer and add uncooked rigatoni, pushing pasta down so liquid covers it.

Cover and cook for 12-14 minutes, stirring every 3 minutes. Check pasta at 12 minutes—it should be al dente with a slight bite in the center. If liquid absorbs too quickly, add ¼ cup water and continue cooking.

Remove from heat and stir in Parmesan and basil. Let the skillet sit for 2 minutes so sauce thickens slightly and clings to pasta. Top with extra cheese and torn basil leaves before serving.