In a large pot, boil pasta according to package directions, making sure you liberally salt the water (about a tbsp or so of salt).
In the last two minutes of cooking time, add in broccoli. Reserve 1/2 cup pasta water, drain, and set aside.
In the same pot, coat bottom with cooking spray and brown sausage until cooked through. Pour into a separate bowl.
In the same pot, heat oil and butter with garlic and red pepper flakes over medium heat for about a minute, or until garlic is fragrant. Add in a few splashes of pasta water to deglaze the pan, then add in pasta, broccoli, and sausage. Mix together.
Off heat, add parmesan and mix again. Add in more pasta water as you feel necessary. Once the pasta is at the consistency you like, taste for seasoning and adjust salt and pepper as needed.