Boil the pasta: Bring a large pot of salted water to a rolling boil. Cook pasta until just shy of al dente, 1 minute less than package directions. Reserve 1 cup of pasta water, then drain.

Season the shrimp: Pat shrimp dry. Toss with 1 tablespoon olive oil, 1/2 teaspoon salt, 1/4 teaspoon black pepper, and smoked paprika if using.

Sear the shrimp: Heat 1 tablespoon olive oil in a large skillet over medium-high. Add shrimp in a single layer. Cook 1–2 minutes per side until just opaque. Transfer to a plate. Do not overcook.

Sauté the garlic: Reduce heat to medium. Add butter and remaining 1 tablespoon olive oil to the skillet. When foamy, add garlic and red pepper flakes. Cook 30–60 seconds until fragrant, stirring constantly. Do not brown the garlic.

Deglaze and build the sauce: Pour in wine or broth, scraping up any browned bits. Simmer 1–2 minutes to reduce slightly. Stir in lemon zest and 2 tablespoons lemon juice.

Emulsify: Add 1/2 cup reserved pasta water. Swirl the pan to combine into a light, glossy sauce.

Toss with pasta: Add drained pasta to the skillet. Toss over medium heat for 1–2 minutes so the sauce clings. If dry, add more pasta water a splash at a time.

Finish with shrimp and cheese: Return shrimp and any juices to the pan. Sprinkle in Parmesan and half the parsley. Toss until shrimp are warmed through and the cheese melts into the sauce. Taste and adjust salt, pepper, and lemon juice.

Serve: Plate immediately. Top with remaining parsley, extra Parmesan, a drizzle of olive oil, and a pinch of red pepper flakes if you like heat.