Preheat your oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
Cook the pasta according to package directions until al dente. Drain and set aside.
In a large skillet, heat olive oil and 2 tablespoons of butter over medium heat.
Add garlic and red pepper flakes. Cook for 1 minute until fragrant.
Add shrimp and cook until just pink, about 2–3 minutes per side. Remove shrimp and set aside.
Add white wine, lemon juice, and zest to the skillet. Simmer for 2–3 minutes, then add remaining 2 tablespoons of butter.
Stir in cooked pasta, shrimp, and parsley. Toss to combine, then season with salt and pepper.
Transfer the mixture to the baking dish. Sprinkle mozzarella and Parmesan evenly on top.
Bake for 12–15 minutes until cheese is bubbly and golden. Garnish with more parsley if desired.