01 - Cook pasta in a large pot of salted boiling water until al dente. Reserve 1/2 cup pasta water, then drain and set aside.
02 - Heat 1 tbsp butter and 1 tbsp olive oil in a large skillet over medium-high heat. Add shrimp in a single layer, season 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. Sauté shallot for 2 minutes until soft. Add garlic and cook for 30 seconds until fragrant.
04 - Pour in white wine, scraping up browned bits from the pan bottom. 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 melts and sauce becomes smooth.
06 - Return shrimp to the skillet. Add cooked pasta and toss to coat. If sauce is too thick, add reserved pasta water. Stir in chopped parsley, season to taste, and serve immediately with extra parsley, Parmesan, and lemon wedges.