Bring a large pot of salted water to a boil. Cook pasta until just al dente. Reserve 1/2 cup water and drain.
Pat shrimp dry. Season with a pinch of salt and black pepper.
Warm olive oil and 1 tablespoon butter in a large skillet over medium-high heat.
Sear shrimp 1–2 minutes per side until just opaque. Transfer to a plate.
Lower heat to medium. Melt remaining butter. Stir in garlic and red pepper flakes; cook 30 seconds until fragrant.
Pour in white wine. Simmer 2–3 minutes, scraping the pan, until reduced by about half.
Stir in lemon juice and zest. Season the sauce with salt and black pepper.
Toss drained pasta into the skillet with a splash of reserved water to loosen the sauce.
Return shrimp to the pan. Add parsley and half the Parmesan. Toss until glossy, adding more water if needed.
Taste and adjust salt, pepper, or lemon. Serve hot with remaining Parmesan.