Cook the pasta according to the package directions. Drain.
Meanwhile, heat the oil in a large skillet over medium-high heat. Cook the onion, stirring often, for 3 minutes.
Add the sausage and cook, stirring, until browned, 2 to 3 minutes.
Add the broccoli and 1 ¼ cups water and simmer, covered, until the broccoli is tender, 5 to 6 minutes.
Toss the pasta with the sausage mixture, including any remaining liquid, and the Parmesan.