Prep the shrimp. Pat the shrimp dry with paper towels.
Toss with a pinch of salt and pepper. Dry shrimp sear better and pick up more flavor.
Boil the pasta. Bring a large pot of salted water to a rolling boil. Cook the pasta until just shy of al dente. Reserve 1/2 cup pasta water, then drain.
Sear the shrimp. In a large skillet, warm 1 tablespoon butter and 1 tablespoon olive oil over medium-high heat.
Add shrimp in a single layer. Cook 1–2 minutes per side until just pink and opaque. Transfer to a plate.
Do not overcook.
Build the sauce base. Reduce heat to medium. Add remaining olive oil and the garlic. Sauté 30 seconds until fragrant, not browned.
Stir in red pepper flakes and lemon zest.
Deglaze. Pour in the white wine or broth, scraping up any browned bits. Let it simmer 1–2 minutes to reduce slightly.
Emulsify with butter. Add the remaining 2 tablespoons butter. Swirl until melted and glossy.
Stir in the lemon juice.
Toss with pasta. Add drained pasta to the skillet with a splash of reserved pasta water. Toss vigorously until the sauce thickens and clings. Add more pasta water a little at a time as needed for a silky coating.
Finish with shrimp and cheese. Return shrimp to the pan.
Sprinkle in Parmesan and parsley. Toss 30–60 seconds. Taste and adjust with salt, pepper, or more lemon.
Serve. Plate immediately.
Top with extra Parmesan, a drizzle of olive oil, and lemon wedges on the side.