Cook the angel hair pasta in salted boiling water until al dente; reserve 1 cup pasta water, then drain.

Heat the olive oil and butter in a large skillet over medium heat. Season the shrimp with a pinch of salt and the black pepper, then sear in a single layer about 2 minutes per side until pink. Transfer to a plate.

Reduce heat to medium-low, add the garlic and red pepper flakes, and cook 30 seconds. Stir in the lemon zest, lemon juice, and 1/2 cup reserved pasta water. Simmer 1 minute.

Return the shrimp and any juices to the skillet, add the pasta and parsley, and toss until coated. Serve immediately with a drizzle of olive oil and extra parsley.