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—pasta will finish cooking in the oven.
03 - In a large skillet over medium heat, melt butter with olive oil. Add minced garlic and chopped 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 and opaque. Do not overcook.
05 - Pour in white wine, scraping up any browned bits from the bottom of the skillet. Simmer for 2 minutes to reduce slightly.
06 - Stir in lemon juice and zest, then add heavy cream. Simmer 2-3 minutes until sauce thickens enough to coat a spoon. Remove from heat and fold in parsley.
07 - Add cooked pasta to the skillet with shrimp sauce. Toss to coat evenly, then stir in 2/3 of the grated parmesan.
08 - Transfer mixture to the prepared baking dish. Top with shredded mozzarella and remaining parmesan cheese.
09 - Bake for 15-18 minutes until cheese is melted, golden, and bubbling around the edges.
10 - Let the dish rest for 5 minutes before serving to set. Garnish with additional fresh parsley and lemon wedges if desired.