Bring a large pot of salted water to a boil and cook pasta al dente. About 2-3 minutes before the pasta is done, add the broccoli florets. This saves a pot and keeps the broccoli tender-crisp.
Melt butter in a skillet over medium-high heat, then whisk in flour and cook for 1-2 minutes. Add garlic, broth, lemon juice, and Italian seasoning. Let it bubble slightly for flavor development.
Whisk in heavy cream and cook until slightly thickened. Stir in freshly grated Parmesan cheese and remove from heat to prevent over-thickening.
Drain pasta and broccoli, then toss them in the skillet with the creamy sauce. Add a splash of pasta water if you want a looser sauce. Season with salt, pepper, and extra Parmesan before serving.