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 aside.
02 - Pat the shrimp thoroughly dry with paper towels. Season evenly with a light dusting of salt and freshly ground black pepper.
03 - In a large skillet set over medium-high heat, melt 2 tbsp butter with 1 tbsp 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 - Return the same skillet to heat and add the remaining 2 tbsp butter and 1 tbsp olive oil. Sauté the thinly sliced garlic and crushed 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 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. Use tongs to toss everything together until the noodles are well coated and the sauce clings to the pasta.
08 - Taste the finished dish and adjust with additional salt, black pepper, or a squeeze of lemon juice as desired.
09 - Divide among warmed plates or shallow bowls. Finish with a generous sprinkle of chopped fresh parsley, grated Parmesan cheese, and a lemon wedge alongside. Serve immediately while hot.