Bring a large pot of salted water to a boil. Add the orecchiette pasta and cook according to package instructions until al dente, usually about 8-10 minutes. In the last 3 minutes of cooking, add the broccoli florets to the pot with the pasta. Once cooked, drain the pasta and broccoli in a colander, reserving 1 cup of the pasta cooking water.
In a large skillet, heat the olive oil over medium heat. Add the Italian sausage, breaking it up with a wooden spoon. Cook until the sausage is browned and cooked through, about 5-7 minutes. Drain excess fat if necessary.
Add the minced garlic and red pepper flakes to the skillet with the sausage. Sauté for about 1 minute until fragrant.
Incorporate the cooked orecchiette and broccoli into the skillet, tossing everything together well. Add reserved pasta water gradually, a little at a time, until the desired sauce consistency is achieved.
Season the dish with salt and freshly ground black pepper to taste. Cook for another 2 minutes, allowing all ingredients to meld together.
Serve hot, topped with grated Parmesan cheese.