Boil a large pot of salted water. Cook fettuccine until al dente. Reserve 1/2 cup pasta water, then drain.
Pat shrimp dry, then season with salt, black pepper, and a pinch of red pepper flakes.
Heat olive oil and 1 tbsp butter in a large skillet over medium-high. Sear shrimp 1–2 minutes per side. Transfer to a plate.
Reduce heat to medium. Add remaining butter, then sauté garlic for 30 seconds until fragrant.
Pour in heavy cream. Simmer gently 2–3 minutes. Whisk in Parmesan until smooth and creamy.
Add drained pasta to the sauce. Toss, splashing in reserved pasta water until glossy and well-coated.
Return shrimp to the pan. Stir in lemon juice and parsley. Taste and adjust salt and pepper.
Serve hot, topped with extra Parmesan.