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 pasta aside.
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 over medium-high heat, melt 2 tbsp butter with 1 tbsp olive oil. Arrange shrimp in a single layer and sear for 1–2 minutes per side until pink and opaque. Transfer shrimp to a plate and set aside.
04 - In the same skillet, add the remaining 2 tbsp butter and 1 tbsp olive oil. Sauté thinly sliced garlic and red pepper flakes for about 1 minute until fragrant, taking care not to let the garlic brown.
05 - Pour in the white wine (or chicken broth) and lemon juice, scraping up any browned bits from the bottom of the skillet. Simmer for 1–2 minutes to reduce slightly, then stir in the lemon zest.
06 - Return the seared shrimp to the skillet and toss to coat evenly in the garlic butter sauce.
07 - Add the drained angel hair pasta to the skillet along with reserved pasta water as needed to loosen the sauce. Toss everything together with tongs until the pasta is well coated and the sauce clings to the noodles.
08 - Taste and adjust with additional salt, pepper, or a squeeze of lemon juice as desired.
09 - Serve immediately on warm plates, garnished with chopped fresh parsley, grated Parmesan cheese, and lemon wedges alongside.