01 - Bring a large pot of salted water to a rolling boil. Cook angel hair pasta according to package directions until al dente. Drain through a colander, reserving 1/2 cup of starchy pasta water. Set aside.
02 - Pat shrimp thoroughly dry with paper towels. Season lightly on both sides with salt and freshly ground black pepper.
03 - In a large skillet over medium-high heat, melt 2 tbsp butter with 1 tbsp olive oil. Arrange shrimp in a single layer and sear for 1 to 2 minutes per side until pink and opaque throughout. Transfer shrimp to a plate and set aside.
04 - In the same skillet, add the remaining 2 tbsp butter and 1 tbsp olive oil. Sauté sliced garlic and red pepper flakes for about 1 minute until fragrant, taking care not to let the garlic brown.
05 - Pour in the white wine or chicken broth along with the lemon juice, scraping up any browned bits from the bottom of the pan. Simmer for 1 to 2 minutes to reduce slightly, then stir in the lemon zest.
06 - Return the seared shrimp to the skillet and toss gently to coat evenly in the garlic butter sauce.
07 - Add the drained angel hair pasta to the skillet along with splashes of reserved pasta water as needed to loosen the sauce. Toss everything together using tongs until the pasta is well coated and the sauce clings to the noodles.
08 - Taste and adjust with additional salt, pepper, or lemon juice as desired. Serve immediately, garnished with chopped fresh parsley, grated Parmesan cheese, and lemon wedges on the side.