Bring a large pot of water to a boil. Add 1 tablespoon salt and the linguine. Cook according to package directions until al dente. Reserve 1 cup pasta water, then drain and set aside.

While the pasta cooks, pat the shrimp dry and season with salt and pepper. In a large skillet over medium-high heat, heat 1 tablespoon olive oil. Add the shrimp in a single layer and cook for 1-2 minutes per side until pink, opaque, and reach an internal temperature of 145°F (63°C). Transfer to a plate.

Reduce heat to medium. In the same skillet, melt 2 tablespoons butter. Add garlic and red pepper flakes; cook until fragrant, about 30 seconds. Stir in lemon juice, lemon zest, and 1/2 cup reserved pasta water. Simmer for 2 minutes to blend flavors.

Return the cooked linguine to the skillet. Add the remaining 1 tablespoon butter and the Parmesan. Toss with tongs until the pasta is well coated and the sauce has thickened slightly. Fold in the cooked shrimp and most of the parsley, reserving some for garnish.

Divide among warm plates, twirling portions into neat nests. Sprinkle with remaining parsley, extra Parmesan, and serve with lemon wedges.