For the Shrimp:
1 tablespoon extra-virgin olive oil
¾ pound large shrimp, peeled and deveined
¼ teaspoon kosher salt
⅛ teaspoon freshly ground black pepper
For the Pasta:
1 pound spaghetti
½ teaspoon kosher salt, plus more for the pasta water
⅔ cup extra-virgin olive oil
⅔ cup grated parmesan cheese, plus more for topping (optional)
1 tablespoon grated lemon zest (about 1 large lemon)
½ cup fresh lemon juice (about 2 large lemons)
¼ teaspoon freshly ground black pepper
⅓ cup chopped fresh basil
2 tablespoons capers, fried
Make the shrimp: In a medium saute pan, heat the olive oil over medium-high heat. Season the shrimp with the salt and pepper; add to the preheated pan in a single layer. Cook for 2 to 3 minutes per side, or until pink and cooked through. Set aside.
Make the pasta: Cook the pasta in a large pot of boiling salted water until tender but still firm to the bite, stirring occasionally to prevent sticking, about 8 minutes. Drain, reserving 1 cup pasta water. Meanwhile, whisk the olive oil, parmesan and lemon zest and juice in a large bowl to blend.
Toss the pasta with the lemon sauce, shrimp and the reserved cooking liquid, adding it ¼ cup at a time as needed to moisten. Season with the salt and pepper; stir in the basil. Garnish with the fried capers and more parmesan, if desired.