Bring a large pot of well-salted water to a rolling boil. Add the pasta and cook until just shy of al dente, approximately 1 to 2 minutes less than the package directions. Drain and set aside.

Heat the olive oil along with 2 tablespoons of the butter in a large skillet set over medium heat. Pat the shrimp dry and season both sides with salt and black pepper. Place shrimp in the skillet and sear for 1 to 2 minutes per side, until opaque and lightly golden. Transfer the cooked shrimp to a separate plate.

In the same pan, melt the remaining 2 tablespoons of butter. Add the minced garlic and crushed red pepper flakes. Sauté briefly for about 30 seconds until aromatic. Pour in the wine (or broth), along with the lemon juice and zest. Allow the mixture to simmer for 2 to 3 minutes until slightly reduced.

Return the drained pasta to the skillet, tossing thoroughly to coat it in the garlic-butter mixture. Stir in half of the grated Parmesan and half of the chopped parsley. Gently fold in the cooked shrimp.

Transfer the combined shrimp and pasta mixture into a lightly greased 9-by-13-inch baking dish. Scatter the shredded mozzarella and the remaining Parmesan evenly across the top.

Place the baking dish, uncovered, into a preheated oven at 375°F (190°C). Bake for 15 minutes, or until the cheese is fully melted and develops a golden hue.

Remove from the oven and garnish with the remaining parsley. Optionally, finish with an additional squeeze of lemon before serving hot.