01 - Bring a large pot of salted water to a rolling boil. Cook the 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 and keep warm.
02 - Pat the shrimp thoroughly dry with paper towels. Season both sides lightly with salt and freshly ground black pepper.
03 - In a large skillet set over medium-high heat, melt 2 tablespoons of butter with 1 tablespoon of olive oil. Arrange the shrimp in a single layer without crowding the pan. 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 medium heat and add the remaining 2 tablespoons of butter and 1 tablespoon of 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) and freshly squeezed lemon juice, using a wooden spoon to scrape up any browned bits from the bottom of the pan. 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 the seasoning with additional salt, black pepper, or a squeeze of fresh lemon juice as desired.
09 - Divide the pasta among serving plates or transfer to a large serving bowl. Finish with a generous sprinkling of chopped fresh parsley, freshly grated Parmesan cheese, and lemon wedges on the side. Serve immediately while hot.