01 - Preheat oven to 400°F. Lightly grease a large baking dish with butter or cooking spray.
02 - Boil pasta in salted water for 2 minutes less than package directions. Drain well and set aside.
03 - Melt butter with olive oil in a large skillet over medium heat. 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 browned bits from the bottom. Simmer for 2 minutes.
06 - Stir in lemon juice and zest. Add heavy cream and simmer 2-3 minutes until slightly thickened. Remove from heat and stir in parsley.
07 - Toss cooked pasta with shrimp sauce and 2/3 of the parmesan cheese until evenly coated.
08 - Transfer mixture to the prepared baking dish. Top with mozzarella and remaining parmesan.
09 - Bake for 15-18 minutes until cheese is melted and golden brown. Let rest 5 minutes before serving.
10 - Garnish with additional fresh parsley and lemon wedges if desired.