Preheat Oven & Cook Pasta:
Preheat your oven to 375°F (190°C). Cook the pasta according to the package instructions until al dente. Drain and set aside.

Cook Shrimp:
Season the shrimp with salt and pepper. In a large skillet over medium heat, melt 2 tablespoons of butter with the olive oil. Add the minced garlic and sauté for about 1 minute until fragrant. Add the shrimp and cook for about 2 minutes per side until they turn pink and opaque. Remove the shrimp from the skillet and set aside.

Prepare the Sauce:
In the same skillet, add the white wine (or chicken broth), lemon juice, heavy cream, red pepper flakes, and the remaining 2 tablespoons of butter. Stir well and let the mixture simmer for 3–4 minutes until it slightly thickens. Stir in 1/4 cup of the Parmesan cheese until melted.

Combine & Assemble:
Add the cooked pasta and shrimp back into the skillet, stirring to evenly coat everything with the sauce. Transfer the mixture into a greased baking dish. Sprinkle the shredded mozzarella and the remaining Parmesan cheese evenly on top.

Bake:
Place the dish in the preheated oven and bake for 10–12 minutes, or until the cheese is melted and bubbly.

Garnish & Serve:
Remove from the oven, garnish with fresh chopped parsley, and serve warm.