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 ½ cup of starchy pasta water. Set pasta aside.
02 - Pat shrimp thoroughly dry with paper towels and 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 1–2 minutes per side until pink and opaque. 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 thinly 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 1–2 minutes to reduce slightly, then stir in the lemon zest.
06 - Return the seared shrimp to the skillet and toss to coat in the sauce. Add the drained pasta along with splashes of the reserved pasta water as needed to loosen the sauce and help it cling to the noodles. Toss everything together until evenly coated.
07 - 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 alongside.