Cook the pasta. Bring a large pot of salted water to a boil. Add the gluten-free pasta and cook until just al dente according to package directions. Be careful not to overcook, as the pasta will continue cooking in the sauce. Before draining, reserve about ½ cup of pasta water. Drain and set aside.
Blanch the broccoli. Using the same pot, bring water back to a boil if needed. Add the broccoli and cook for 2–3 minutes until bright green and just tender. Drain and set aside.
Cook the sausage. In the same pot (or a large skillet), heat olive oil over medium heat. Add the Italian sausage and cook until browned and fully cooked, breaking it into small pieces as it cooks. If there is excess grease, carefully drain it.
Add garlic and seasoning. Push the sausage to one side of the pan. Add a little more olive oil if needed, then add the garlic and crushed red pepper flakes. Cook for 1–2 minutes until fragrant, being careful not to burn the garlic.
Build the sauce. Pour in the white wine and let it simmer for a few minutes to reduce slightly. Add the chicken stock and broccoli, then stir everything together and cook for another 3–5 minutes until the broccoli is tender.
Finish the dish. Stir in the butter until melted. Add the cooked pasta and toss everything together until well combined. If needed, add a splash of reserved pasta water to help the sauce coat the pasta.
Serve. Remove from heat and stir in the Parmesan cheese. Taste and season with salt and black pepper as needed. Serve warm with extra Parmesan on top.