Preheat Oven: Set the oven to 375°F (190°C).
Cook Pasta: Cook the pasta according to the package instructions until al dente, then drain and set aside.
Sauté Aromatics: In a large skillet, melt the butter over medium heat. Add the minced garlic and red pepper flakes, sautéing for about 1 minute until fragrant.
Cook Shrimp: Add the shrimp to the skillet and cook for 3-4 minutes, or until they turn pink and opaque. Remove the shrimp and set them aside.
Prepare Sauce: Pour the white wine (or chicken broth) into the skillet, scraping up any browned bits from the bottom of the pan. Let it simmer for 2 minutes.
Combine Flavors: Stir in the lemon juice, lemon zest, and heavy cream, then bring the mixture to a gentle simmer.
Toss Pasta: Add the cooked pasta to the skillet and toss to coat it in the creamy sauce. Season with salt and pepper to taste.
Assemble Dish: Transfer the pasta to a large baking dish, spreading it evenly. Arrange the cooked shrimp on top.
Add Cheese: Sprinkle the grated Parmesan and shredded mozzarella over the pasta and shrimp.
Bake: Place the dish in the preheated oven and bake for 15-20 minutes, or until the cheese is melted and bubbly.
Garnish and Serve: Remove from the oven, garnish with chopped fresh parsley, and serve immediately.