Preheat the oven to 400°F (200°C).
Cook the fettuccine according to package instructions until al dente, then drain and set aside.
In a large skillet, melt the butter over medium heat. Add the minced garlic and sauté for 1-2 minutes until fragrant.
Pour in the white wine, and add red pepper flakes, salt, and pepper. Cook for an additional 3-4 minutes until the wine has reduced slightly.
Add the shrimp to the skillet, cooking until they turn pink and opaque, about 3-5 minutes.
In a large mixing bowl, combine the cooked fettuccine, shrimp mixture, chopped parsley, and half of the grated Parmesan cheese.
Transfer the pasta and shrimp mixture to a baking dish, spreading it evenly. Top with the remaining Parmesan cheese.
Bake in the preheated oven for 15-20 minutes until bubbly and golden.
Remove from the oven and let sit for a few minutes before serving. Garnish with additional parsley if desired.