Prep the shrimp and aromatics: Pat the shrimp dry and season with a pinch of salt and pepper. Zest both lemons, then juice them (you should get about 1/4 to 1/3 cup juice). Slice or mince the garlic. Chop the parsley.

Warm the base: In a large, deep skillet or wide pot, heat 2 tablespoons olive oil over medium heat. Add the garlic and a pinch of red pepper flakes. Cook 30–60 seconds until fragrant, not browned.

Build the cooking liquid: Pour in the broth, 1/4 cup lemon juice, and half the lemon zest. Add 1/2 teaspoon salt to start. Bring to a lively simmer.

Add the pasta: Lay the pasta in the pan. If it doesn’t fit, nudge it down as it softens. Stir and separate strands to prevent sticking. Cook at a steady simmer, uncovered, stirring often, until al dente (usually 8–10 minutes). If liquid gets too low before pasta is done, add a splash of hot water or more broth.

Finish the sauce: When the pasta is just shy of al dente, add the butter. Toss until melted and glossy. Taste and adjust with more lemon juice, salt, or pepper. The sauce should be lightly thickened and cling to the noodles.

Cook the shrimp: Push pasta to the sides to make a well. Add a drizzle of olive oil if the pan looks dry. Add shrimp in a single layer and cook 1–2 minutes per side, just until pink and opaque. Toss shrimp through the pasta.

Brighten and serve: Stir in remaining lemon zest and most of the parsley. If you like, add a handful of Parmesan to enrich the sauce. Twirl into bowls, sprinkle with extra parsley, black pepper, and Parmesan. Serve immediately with lemon wedges.