Wash hands with soap and water. Fill a medium pot 3/4 of the way up with salted water; cover and heat to boiling on high. Peel and chop the onion. Wash and dry the broccoli, then cut the florets from the stem.

Heat a little oil in a pan over medium-high heat, add the sausage. Cook, stirring occasionally and breaking the meat apart with a spoon, 6 to 8 minutes, or until browned. Add the onion and garlic and season with salt and pepper. Cook, stirring frequently, 1 to 2 minutes, or until softened and the sausage is cooked through.

Add the vinegar and cream. Cook, stirring frequently and scraping up any browned bits, 30 seconds to 1 minute, or until combined. Turn off the heat.

Meanwhile, add the pasta to the pot of boiling water. Cook, uncovered, 6 minutes. Add the broccoli. Cook for 4 to 6 minutes, or until the broccoli is tender and the pasta is done. Turn off the heat. Reserving 1/2 cup of the cooking water, drain thoroughly.

To the pan of cooked sausage and sauce, add the cooked pasta and broccoli and half the reserved cooking water. Cook on medium-high, stirring constantly, 1 to 2 minutes, or until combined and the pasta is coated (if necessary, gradually add the remaining cooking water to ensure the pasta is thoroughly coated).

Turn off the heat. Taste, then season with salt and pepper, if desired. Serve the finished pasta with parmesan. This recipe makes 6 servings. Refrigerate leftovers within 2 hours.