Preheat the oven to 375°F (190°C).
Cook the pasta according to package directions. Drain and set aside.
In a large skillet, heat olive oil over medium heat. Add shrimp and cook for 2–3 minutes until pink.
Add garlic and red pepper flakes, cooking for another 30 seconds.
Pour in wine (or broth) and lemon juice. Stir in salt and pepper. Simmer for 2–3 minutes.
Add butter and stir until melted. Mix in parsley and cooked pasta.
Transfer everything to a greased 9×13-inch baking dish. Top with mozzarella and Parmesan.
Bake uncovered for 15–20 minutes until the cheese is bubbly and golden.
Garnish with extra parsley before serving, if desired.