01 - Bring a large pot of salted water to a boil. Cook angel hair pasta according to package directions until al dente. Reserve 1/2 cup of the starchy pasta water, then drain and set aside.
02 - Pat the shrimp completely dry with paper towels. Season evenly with salt, black pepper, and red pepper flakes if using.
03 - In a large skillet over medium-high heat, melt 1 tablespoon butter with 1 tablespoon olive oil. Arrange shrimp in a single layer and cook for 1 to 2 minutes per side until pink and opaque throughout. Transfer to a plate and cover loosely.
04 - Return the skillet to medium heat and add remaining butter and olive oil. Add minced garlic and sauté for 30 seconds until fragrant, taking care not to brown or burn it.
05 - Stir in lemon zest, lemon juice, and white wine. Use a wooden spoon to scrape up any browned bits from the bottom. Simmer for 1 to 2 minutes until slightly reduced.
06 - Return the shrimp to the skillet. Add the drained pasta and toss gently with tongs to coat everything in the sauce. Add reserved pasta water a tablespoon at a time if needed to achieve a silky consistency.
07 - Stir in fresh parsley. Taste and adjust seasoning with additional salt and pepper if desired. Serve immediately in warmed bowls with extra lemon wedges on the side.