Cook the pasta in salted boiling water until al dente. Reserve 1 cup pasta water, then drain.
Pat the shrimp dry and season with salt and pepper.
Heat the olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Cook the shrimp 1–2 minutes per side, until pink. Transfer to a plate.
Reduce the heat to medium. Add the remaining butter, garlic, and red pepper flakes and cook 1 minute.
Add the lemon zest, lemon juice, and ½ cup pasta water. Simmer 1–2 minutes.
Add the pasta and Parmesan and toss, adding more pasta water as needed for a glossy sauce.
Return the shrimp to the pan, sprinkle with parsley, and toss. Serve with extra lemon wedges.