Prep the shrimp: Pat the shrimp dry with paper towels. Season with a big pinch of salt, a few grinds of black pepper, and the smoked paprika if using. Dry shrimp sear better and stay juicy.

Boil the pasta: Bring a large pot of salted water to a rolling boil. Add pasta and cook until al dente, about 1–2 minutes less than package directions. Reserve 1 cup of pasta water before draining.

Sear the shrimp: In a large skillet over medium-high heat, warm 1 tablespoon olive oil and 1 tablespoon butter. Add shrimp in a single layer and cook 1–2 minutes per side until just opaque and lightly golden. Transfer to a plate. Don’t overcook.

Build the flavor base: Lower heat to medium. Add remaining olive oil and 2 tablespoons butter to the same skillet. Add garlic and red pepper flakes. Cook 30–60 seconds until fragrant, stirring constantly. Don’t brown the garlic or it will taste bitter.

Deglaze: Pour in the white wine (or broth), scraping up any browned bits. Simmer 2–3 minutes to reduce by about half. This concentrates flavor and cooks off the alcohol.

Emulsify the sauce: Add 1/2 cup reserved pasta water and the lemon zest. Bring to a gentle simmer. Whisk in the last tablespoon of butter until the sauce looks glossy.

Toss the pasta: Add drained pasta to the skillet. Toss for 1–2 minutes so the sauce coats every strand. If it looks dry, splash in more pasta water a few tablespoons at a time.

Add shrimp and finish: Return shrimp to the pan with any juices. Add lemon juice, Parmesan, and most of the parsley. Toss until the shrimp are warmed through and the cheese melts smoothly into the sauce. Taste and adjust salt, pepper, and lemon.

Serve: Twirl into bowls. Top with extra Parmesan, the remaining parsley, and a drizzle of olive oil if you like. Serve immediately with lemon wedges.