01 - Preheat oven to 400°F. Lightly grease a large baking dish with butter or cooking spray.
02 - Bring a large pot of salted water to boil. Cook pasta 2 minutes less than package directions, as it will finish cooking in the oven. Drain well and set aside.
03 - In a large skillet over medium heat, melt butter with olive oil. Add garlic and shallot, sauté until fragrant, about 1-2 minutes.
04 - Add shrimp to the skillet. Season with salt, pepper, and red pepper flakes. Cook 2-3 minutes until just pink—do not overcook.
05 - Pour in white wine, scraping up any browned bits from the bottom of the pan. Simmer for 2 minutes to reduce slightly.
06 - Add lemon juice and zest to the skillet. Stir in heavy cream and simmer 2-3 minutes until slightly thickened. Remove from heat and stir in parsley.
07 - Add cooked pasta to the skillet with the shrimp sauce. Add 2/3 of the parmesan cheese. Toss everything together until pasta is evenly coated.
08 - Transfer the pasta mixture to the prepared baking dish. Sprinkle mozzarella cheese and remaining parmesan evenly over the top.
09 - Bake for 15-18 minutes until the cheese is melted, golden brown, and bubbling around the edges.
10 - Let the dish rest for 5 minutes before serving. Garnish with additional fresh parsley and serve with lemon wedges if desired.