Preheat the oven to 400°F (200°C) and prepare a baking sheet.
Toss the broccoli florets with olive oil, salt, and pepper.
Roast the broccoli in the preheated oven for about 20-25 minutes, until tender and crispy.
Cook the fettuccine according to package instructions until al dente and reserve about 1 cup of pasta water before draining.
In a large skillet over medium heat, melt 2 tablespoons of butter and add the minced garlic, sautéing for about 1 minute.
Add shrimp to the skillet, seasoning with salt and pepper. Cook until shrimp are pink, about 2-3 minutes per side.
Reduce heat to low and pour in the heavy cream, stirring to combine.
Stir in the remaining butter and Parmesan cheese until melted and smooth.
Add the cooked fettuccine to the sauce, tossing to coat. If needed, add reserved pasta water to reach desired consistency.
To serve, plate the pasta and top with roasted broccoli and red pepper flakes if desired.