Bring pot of salted water to a boil. Cook pasta until Al Dente, about 10 minutes or as package lable directs. Add broccoli for the last 2 minutes of cooking time.
While pasta is cooking, warm olive oil in a large skillet over medium heat. Add sausage and cook, breaking it up into small pieces with a wooden spoon, until brown and cooked through, 8 to 10 minutes. Add garlic and cook, stirring until fragrant, about 2 minutes.
Reserve 1 cup cooking liquid; drain pasta and broccoli, add to skillet with 1/2 cup reserved water and toss well. Sprinkle Parmesan on top and toss. *Add more liquid if necessary to moisten. Season with salt and pepper. Serve with additional parmesan if desired.