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 10-12 minutes. In the last 3-4 minutes of cooking, add the broccoli florets to the boiling pasta. Once done, drain in a colander and set aside.
In a large skillet, heat the olive oil over medium heat. Remove the sausage from its casings and crumble it into the skillet. Cook, stirring often, until fully browned and cooked through, about 6-8 minutes.
Add the minced garlic to the skillet with the sausage and cook for an additional 1-2 minutes, until fragrant.
Add the drained orecchiette and broccoli to the skillet. Toss everything together until well combined. Season with salt, black pepper, and red pepper flakes (if using). Cook for an additional 2-3 minutes to heat through.
Remove from heat, sprinkle with grated Parmesan cheese, and toss again to incorporate. Adjust seasoning if needed.
Divide the orecchiette with sausage and broccoli among four serving plates. Serve hot and enjoy!