01 - Bring a large pot of salted water to a boil. Cook pasta according to package directions until al dente. Reserve 1/2 cup pasta water before draining.
02 - Pat shrimp completely dry with paper towels. Season evenly with kosher salt and freshly ground black pepper.
03 - Heat 2 tbsp olive oil in a large skillet over medium-high heat. Arrange shrimp in a single layer. Cook 1-2 minutes per side until pink and just cooked through. Transfer to a plate.
04 - Reduce heat to medium. Add remaining 1 tbsp olive oil to the skillet. Sauté garlic, lemon zest, and red pepper flakes for 1 minute until fragrant, being careful not to burn the garlic.
05 - Pour in white wine or broth. Simmer for 2-3 minutes, scraping up any browned bits from the bottom of the skillet.
06 - Add lemon juice and butter. Stir constantly until butter melts and sauce begins to emulsify.
07 - Return shrimp to the skillet. Add drained pasta and toss thoroughly to coat. Add reserved pasta water as needed to achieve silky sauce consistency.
08 - Remove from heat. Stir in fresh parsley and sprinkle with Parmesan. Serve immediately with lemon wedges on the side.