Boil salted water in a large pot. Cook fettuccine until al dente (10–12 minutes). Drain and set aside, saving ½ cup of pasta water.
Steam broccoli in a covered saucepan with a splash of water for 4–5 minutes, until tender. Drain and set aside.
Melt 1 tbsp butter in a skillet over medium heat. Cook shrimp 2–3 minutes per side until pink. Remove and keep warm.
Add remaining butter to the skillet. Sauté garlic for 1 minute, then whisk in flour to form a thick, golden paste.
Pour in white wine, scraping the pan and whisking until smooth. Simmer for 2 minutes.
Lower heat. Slowly whisk in heavy cream. Simmer 3–4 minutes, then add parmesan. Stir until creamy and smooth.
Add shrimp, broccoli, and pasta. Toss gently to coat. Thin sauce with pasta water if needed.
Serve hot with extra parmesan and chopped parsley, if desired.