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 the starchy pasta water. Set the pasta aside.
02 - Pat the shrimp thoroughly dry with paper towels. Season evenly with a light dusting of salt and freshly ground black pepper on both sides.
03 - Set 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 approximately 1 minute until fragrant, taking care not to let the garlic brown.
05 - Pour in the dry white wine (or chicken broth) and freshly squeezed lemon juice, scraping up any caramelized bits from the bottom of the pan. Let the liquid simmer for 1 to 2 minutes to reduce slightly. 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 and help it cling to the noodles. Toss everything together using tongs until the pasta is thoroughly coated.
08 - Taste the finished dish and adjust with additional salt, pepper, or a squeeze of lemon juice as desired.
09 - Divide among serving plates immediately. Finish each portion with a generous sprinkle of chopped fresh parsley, freshly grated Parmesan cheese, and a lemon wedge on the side.