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 1/4 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.
Photograph by Linda Xiao
How to Fry Capers: Drain, rinse and dry the capers very well. Heat 1/4 inch vegetable oil in a small straight-sided skillet over medium-high heat until shimmering. Add the capers and fry for about 2 minutes, or until they have popped open and are golden brown and crispy. Using a slotted spoon, remove to a paper towel-lined plate to drain.