1 tablespoon olive oil
1 pound uncooked Italian chicken or turkey sausage, casings removed
1 medium yellow onion, medium dice
Freshly ground black pepper
1 pound broccoli, stemmed and cut into 1-inch florets
1 pound fusilli or other short pasta
3/4 cup heavy cream
1/2 cup tightly packed, finely grated Parmesan cheese (about 1 1/2 ounces), plus more for serving
Bring a large pot of heavily salted water to a boil over high heat. Meanwhile, heat the oil in a large frying pan over medium-high heat until shimmering. Add the sausage and cook, breaking up the meat into smaller pieces with a wooden spoon, until itís no longer pink and is starting to brown, about 6 to 8 minutes. Remove with a slotted spoon to a large bowl and set aside.
Reduce the heat to medium, add the onions, and season with salt and pepper. Cook, stirring occasionally, until the onions have softened and are just starting to brown, about 6 minutes. Turn off the heat.
When the water is boiling, add the broccoli and cook until crisp-tender, about 3 minutes. Using the slotted spoon, transfer the broccoli to the bowl with the sausage.
Return the water to a boil, add the pasta, and cook according to the package directions or until al dente. Reserve 1/2 cup of the pasta water, drain, and return the pasta to the pot; set aside.
Return the pan of onions to medium heat, add the cream, and stir, scraping up any browned bits from the bottom of the pan. Bring to a simmer and cook until slightly thickened, about 2 to 3 minutes. Add the sausage and broccoli and stir until combined.
Pour the broccoli-sausage mixture over the pasta, add the measured Parmesan and reserved pasta water, and stir to combine. Taste and season with salt and pepper as needed. Serve immediately, passing more Parmesan on the side.