Prepare the Shrimp: Pat the shrimp dry and season both sides with salt and pepper.
Cook the Pasta: Bring salted water to a boil and cook angel hair pasta according to package directions. Drain, reserving ¼ cup of pasta water.
Sear the Shrimp: Heat olive oil in a skillet over medium-high heat. Cook shrimp for 1–2 minutes per side until pink and opaque. Remove and set aside.
Make the Sauce: In the same skillet, melt butter. Add garlic and red pepper flakes, cooking just until fragrant. Pour in white wine and simmer for 2–3 minutes. Add lemon juice and zest.
Combine: Return shrimp to the pan. Add pasta and a splash of pasta water. Toss until evenly coated.
Finish: Sprinkle with parsley, garnish with Parmesan and lemon wedges, and serve hot.