Remove shell from shrimp leaving tail shell intact. Rinse and pat dry.
In a food processor combine basil, cheese, garlic, pine nuts, lemon juice, lemon zest and ¼ C olive oil. Slowly drizzle in the remaining ¼ C olive oil while the food processor is running. Season with kosher salt and fresh ground pepper to taste.
Place shrimp in large ziploc bag. Add approx ¼ C lemon pesto - enough to coat all of the shrimp. Refrigerate for at least 1 hour.
Turn on bbq. Thread 3-4 shrimp on metal skewers and lightly season with S&P. Grill each side for approx 2 minutes per side until cooked. Serve with remaining lemon pesto on the side.
Recipe by Good Thyme Kitchen at https://www.goodthymekitchen.com/lemon-pesto-shrimp-skewers/