1½ pounds extra-large shrimp (21/25 per pound), peeled, deveined and patted dry
1 cup lightly packed fresh basil
⅓ cup lightly packed fresh tarragon
3 medium garlic cloves
1½ teaspoons grated lemon zest, plus 1 tablespoon lemon juice
½ teaspoon salt
½ teaspoon black pepper
kosher salt and ground black pepper
¾ cup extra-virgin olive oil
Thread the shrimp onto eight 8- to 10-inch metal skewers, dividing them evenly; skewer each shrimp in a C shape, piercing through 2 points. Place the skewers on a rimmed baking sheet or in a large baking dish.
In a blender, combine the basil, tarragon, garlic, lemon zest, and salt & pepper. Pulse until chopped.
Scrape down the sides, add the oil and puree until bright green and almost smooth, about 30 seconds. Transfer to a small bowl.
Prepare a charcoal or gas grill. For a charcoal grill, ignite a large chimney filled ¾ full of coals, let burn until lightly ashed over, then distribute the coals evenly over the grill bed; open the bottom grill vents and the lid vent.
Heat the grill, covered, for 5 minutes, then clean and oil the cooking grate. For a gas grill, turn all burners to high and heat, covered, for 15 minutes, then clean and oil the cooking grate.
In another small bowl, stir together ½ cup of the herb puree, 1 teaspoon salt and ½ teaspoon pepper, then slather onto the shrimp, coating both sides.
Grill the skewers until the shrimp turn opaque and are lightly charred, 2 to 3 minutes.
Flip and continue to cook until the shrimp are just opaque, about another 2 to 3 minutes.
Transfer the skewers to a serving platter. Stir the lemon juice into the remaining herb puree and drizzle over the shrimp.