Cook the pasta according to package instructions until al dente, then drain.
In a large skillet, melt butter over medium heat and sauté the minced garlic until fragrant.
Add the red pepper flakes and shrimp to the skillet, cooking for about 2-3 minutes until the shrimp begins to turn pink.
Pour in the white wine and let it simmer for 2-3 minutes to reduce slightly.
Stir in the heavy cream, cooking until the mixture is smooth and slightly thickened.
Add the cooked pasta to the skillet, then fold in the mozzarella and Parmesan cheese.
Season with salt and black pepper to taste, and mix everything until well incorporated.
Transfer the mixture to a baking dish and top with remaining mozzarella and a sprinkle of parsley.
Bake in a preheated oven at 350°F (175°C) for about 25-30 minutes, or until bubbly and golden.
Remove from the oven and let it cool slightly before serving.