Cook the fettuccine according to package instructions until al dente.
In a large skillet, melt the butter over medium heat.
Add minced garlic and sauté until fragrant, about 1 minute.
Pour in the heavy cream and bring to a simmer.
Stir in the Parmesan cheese, stirring until melted and smooth.
Add the shrimp and cook until they turn pink, about 3-5 minutes.
Toss in the broccoli and cook for an additional 2-3 minutes until tender.
Combine the cooked fettuccine with the sauce and shrimp mixture.
If the sauce is too thick, add reserved pasta water a little at a time until desired consistency is reached.
Season with salt and pepper to taste before serving.