01 - Cook the pasta in a large pot of salted boiling water until al dente. Reserve 1/2 cup pasta water, then drain and set aside.
02 - While the pasta cooks, heat 1 tablespoon butter and 1 tablespoon olive oil in a large skillet over medium-high heat. Add the shrimp in a single layer, season lightly with salt and pepper, and cook for 1-2 minutes per side until just pink and opaque. Remove shrimp and set aside.
03 - In the same skillet, add remaining butter and olive oil. Add shallot and sauté for 2 minutes until soft. Add garlic and cook for 30 seconds until fragrant.
04 - Pour in the white wine, scraping up any browned bits. Let simmer for 2-3 minutes until slightly reduced.
05 - Lower heat to medium-low. Add heavy cream, lemon zest, lemon juice, red pepper flakes, and Parmesan. Stir until cheese is melted and sauce is smooth.
06 - Return shrimp to the skillet. Add cooked pasta and toss to coat in the sauce. If sauce is too thick, add a splash of reserved pasta water. Stir in chopped parsley. Season to taste with salt and pepper. Serve immediately, garnished with extra parsley, Parmesan, and lemon wedges.