01 - Preheat oven to 400°F and lightly grease a large baking dish with butter or oil.
02 - Boil pasta in salted water for 2 minutes less than package directions. Drain well and set aside—it will finish cooking in the oven.
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, seasoning 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 - Stir in lemon juice and zest, then pour in heavy cream. Simmer 2-3 minutes until sauce begins to thicken. Remove from heat and mix in parsley.
07 - Toss the cooked pasta with the shrimp sauce and two-thirds of the parmesan cheese until evenly coated.
08 - Transfer the mixture to the prepared baking dish. Sprinkle mozzarella and remaining parmesan evenly over the top.
09 - Bake for 15-18 minutes until the cheese is melted, golden, and bubbling. Allow to rest for 5 minutes before serving.
10 - Garnish with additional fresh parsley and serve with lemon wedges on the side if desired.