01 - Bring a large pot of generously salted water to a rolling boil. Add the angel hair pasta and cook according to package directions until al dente. Reserve ½ cup of the starchy pasta water before draining. Set the drained pasta aside.
02 - Pat the shrimp thoroughly dry with paper towels. Season both sides lightly with salt and freshly ground black pepper.
03 - Heat a large skillet over medium-high heat. Melt 2 tbsp of butter with 1 tbsp of olive oil. Arrange the shrimp in a single, even layer and sear for 1 to 2 minutes per side until they turn pink and become opaque throughout. Transfer the shrimp to a plate and set aside.
04 - In the same skillet, add the remaining 2 tbsp of butter and 1 tbsp of olive oil. Sauté the sliced garlic and red pepper flakes for about 1 minute until fragrant, taking care not to let the garlic brown.
05 - Pour in the dry white wine or chicken broth along with the lemon juice, scraping up any caramelized bits from the bottom of the pan. Let the liquid simmer and reduce for 1 to 2 minutes. 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 the reserved pasta water as needed to loosen the sauce. Toss everything together until the pasta is well coated and the sauce reaches a silky consistency.
08 - Taste and adjust the seasoning with additional salt, pepper, or lemon juice as desired. Serve immediately, garnished with chopped fresh parsley, grated Parmesan cheese, and lemon wedges alongside.