Boil the shrimp for 3 minutes, or until they turn pink.
Drain, rinse under cold water to stop the cooking, and transfer to a large bowl.
Place the basil, garlic, lemon zest, lemon juice, pine nuts, and cheese in a blender or food processor and pulse until the mixture is finely chopped.
With the machine running, slowly add the olive oil and process until the pesto is emulsified. If it’s too thick, add more oil, one tablespoon at a time.
Season with salt and pepper to taste.
Pour desired amount over the shrimp—you may not need it all, and toss to coat.
Sprinkle with additional cheese and a drizzle of olive oil at the table.