Bring a large pot of salted water to a boil. Add the pasta, and cook according to package instructions until al dente.
Meanwhile, heat the olive oil in a large skillet, and add the sausage, breaking it up into crumbles with a wooden spoon. Cook until nicely browned and crispy. Add the garlic and cook for 1 minute. Then add the broccoli, chicken broth, and pepper. Stir and cook for about 5-7 minutes, until most of the broth has cooked off and the broccoli is tender.
Use a strainer to transfer the pasta from the boiling water to the skillet. Off the heat, add the butter and parmesan and toss well, adding pasta water as needed to keep the sauce smooth and silky. Serve immediately!