Boil pasta in salted water until al dente. Reserve pasta water, then drain.
Pat shrimp dry. Season with half the salt and the black pepper.
Heat olive oil and 1 tablespoon butter in a large skillet over medium-high.
Sear shrimp 1–2 minutes per side until just pink. Transfer to a plate.
Lower heat. Melt remaining butter. Sauté garlic and red pepper flakes 30 seconds.
Pour in white wine. Simmer and reduce by half, about 2 minutes.
Stir in lemon juice and zest. Add drained pasta and a splash of pasta water.
Return shrimp. Toss with parsley and Parmesan. Adjust salt, pepper, and sauce with water.