Bring a large pot of salted water to a boil. Dice the onion, mince the garlic, and remove sausage from casings if needed. Grate the Parmesan and tear the basil.

Heat olive oil in a large deep skillet over medium-high heat. Add the sausage and break it up with a wooden spoon. Cook for 6-8 minutes until deeply browned and crispy in spots. Transfer to a plate with a slotted spoon, leaving the fat behind.

Reduce heat to medium. Add the onion to the skillet and cook for 4 minutes until softened and starting to turn golden at the edges. Add the garlic and red pepper flakes if using, and cook for 30 seconds until fragrant.

Stir in the tomato paste and cook for 1 minute, scraping up any browned bits from the bottom of the pan. The paste should darken slightly and smell sweet.

Pour in the heavy cream and chicken broth, stirring to combine. Bring to a gentle simmer and cook for 5 minutes until slightly thickened. The sauce should coat the back of a spoon.

While the sauce simmers, cook the pasta in the boiling water until just shy of al dente, about 2 minutes less than package directions. Reserve 1 cup of pasta water, then drain.

Add the pasta and sausage to the skillet with the sauce. Toss over medium heat for 2 minutes, adding splashes of reserved pasta water as needed to loosen. Remove from heat and stir in the Parmesan until melted. Taste and adjust seasoning. Serve immediately topped with fresh basil and extra Parmesan.