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 for al dente texture. Drain thoroughly in a colander and set aside.
03 - In a large skillet over medium heat, melt butter with olive oil. Add minced garlic and chopped shallot, sautéing until fragrant and translucent, about 1-2 minutes.
04 - Add shrimp to the skillet. Season with salt, pepper, and red pepper flakes. Cook for 2-3 minutes until shrimp turn pink and opaque. Avoid overcooking to prevent rubbery texture.
05 - Pour white wine into the skillet, scraping up any browned bits from the bottom. Let simmer for 2 minutes to allow alcohol to evaporate and flavors to concentrate.
06 - Stir in lemon juice and zest. Pour in heavy cream and simmer for 2-3 minutes until sauce thickens slightly. Remove from heat and fold in fresh parsley.
07 - Transfer cooked pasta to the skillet with shrimp sauce. Add 2/3 of the grated parmesan. Toss thoroughly until pasta is evenly coated.
08 - Pour the pasta mixture into the prepared baking dish. Sprinkle shredded mozzarella and remaining parmesan evenly over the top.
09 - Bake for 15-18 minutes until cheese is melted, golden brown, and bubbling around the edges.
10 - Let the dish rest for 5 minutes before serving to allow flavors to settle. Garnish with additional fresh parsley and lemon wedges if desired.