Preheat the oven to 400°F (200°C).
Toss the broccoli with olive oil, salt, and pepper in a bowl.
Spread the broccoli in a single layer on a baking sheet and roast for 20-25 minutes.
While the broccoli is roasting, cook the fettuccine in a large pot of salted water until al dente.
In a large skillet, melt the butter over medium heat.
Add minced garlic to the skillet and sauté until fragrant, about 1 minute.
Pour in the heavy cream and bring to a simmer.
Stir in the grated parmesan cheese until melted and smooth.
Season the sauce with salt, pepper, and red pepper flakes, adjusting to taste.
Add the cooked fettuccine and shrimp to the skillet, tossing to coat.
Serve immediately with roasted broccoli on the side.