01 - Bring a large pot of salted water to a rolling boil. Cook angel hair pasta according to package directions until al dente. Reserve ½ cup of the starchy pasta water before draining. Set the pasta aside.
02 - Pat the shrimp thoroughly dry with paper towels. Season evenly with a light pinch of salt and freshly ground black pepper.
03 - In 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. 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 - Return the same skillet to heat and add the remaining 2 tbsp of butter and 1 tbsp of olive oil. Sauté the thinly sliced garlic and red pepper flakes for approximately 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 fresh lemon juice, scraping up any caramelized bits from the bottom of the skillet. Let the liquid 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 each piece 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 the finished dish and adjust with additional salt, black pepper, or a squeeze of lemon juice as desired.
09 - Serve immediately in warm bowls, garnished with chopped fresh parsley, grated Parmesan cheese, and lemon wedges alongside.