Step 1: Preheat oven to 375°F (190°C). Cook pasta according to package directions until al dente. Drain and set aside.
Step 2: While pasta cooks, pat shrimp dry with paper towels. In a large skillet, melt 2 tablespoons butter and 1 tablespoon olive oil over medium-high heat.
Step 3: Add minced garlic and red pepper flakes (if using) to the skillet and sauté for 1 minute until fragrant.
Step 4: Add shrimp to the skillet and cook for 2-3 minutes per side, until pink and opaque. Do not overcrowd the pan; cook in batches if necessary.
Step 5: Deglaze the pan with white wine or chicken broth, scraping up any browned bits. Stir in lemon juice, remaining 2 tablespoons butter, and 1 tablespoon olive oil until butter is melted. Season with salt and pepper.
Step 6: Add the cooked pasta and chopped fresh parsley to the skillet with the shrimp and sauce. Toss gently to combine all ingredients evenly.
Step 7: Transfer the shrimp and pasta mixture to a 9x13-inch baking dish. Sprinkle evenly with shredded mozzarella and grated Parmesan cheese.
Step 8: Bake for 15-20 minutes, or until the cheese is melted and bubbly and the sauce is heated through. If desired, broil for the last 2-3 minutes for a golden-brown crust (watch carefully to prevent burning).
Step 9: Remove from oven, let rest for a few minutes, then garnish with additional fresh parsley before serving hot.