Preheat the oven to 350°F (175°C).
Cook the pasta according to package directions until al dente; drain and set aside.
In a large skillet, melt the butter over medium heat. Add minced garlic and sauté until fragrant, about 1 minute.
Add the shrimp to the skillet and cook until they turn pink, about 3-4 minutes. Pour in the white wine and let it simmer for 2-3 minutes.
Stir in heavy cream, Parmesan cheese, and red pepper flakes into the skillet. Season with salt and pepper, mixing well until creamy.
Combine the cooked pasta with the shrimp and sauce, mixing to coat everything evenly.
Transfer the pasta mixture to a baking dish and sprinkle with breadcrumbs and additional Parmesan cheese.
Bake in the preheated oven for 25-30 minutes, or until golden and bubbly.
Remove from the oven and let cool for a few minutes before serving. Garnish with fresh parsley before serving.