01 - Preheat oven to 400°F. Lightly grease a large baking dish with butter or cooking spray.
02 - Cook pasta in salted boiling water 2 minutes less than package directions. 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, 1-2 minutes.
04 - Stir in shrimp, season with salt, pepper, and red pepper flakes. Cook 2-3 minutes until just pink. Do not overcook.
05 - Add white wine, scraping up any browned bits from the bottom. Simmer for 2 minutes.
06 - Stir in lemon juice and zest, then pour in heavy cream. 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 prepared baking dish. Sprinkle mozzarella and remaining parmesan evenly over the top.
09 - Bake 15-18 minutes until cheese is melted and golden brown. Let rest 5 minutes before serving.
10 - Garnish with additional fresh parsley and serve with lemon wedges if desired.