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 shrimp thoroughly dry with paper towels and season lightly with salt and freshly ground black pepper on both sides.
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 to 2 minutes per side until pink and fully opaque. Transfer to a plate and set aside.
04 - In the same skillet, add the remaining 2 tbsp butter and 1 tbsp olive oil. Sauté sliced garlic and red pepper flakes for 1 minute until fragrant, taking care not to let the garlic brown.
05 - Pour in the white wine or chicken broth along with the lemon juice, scraping up any caramelized bits from the bottom of the pan. Simmer for 1 to 2 minutes until slightly reduced, then stir in the lemon zest.
06 - Return the seared shrimp to the skillet and toss gently to coat 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 each strand is well coated.
08 - Taste and adjust the seasoning 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.