Roughly chop the basil leaves and palce in a blender or a food processor.

Add the tarragon, cilantro, fennel fronds, chives, parsley, lemon zest, oil, salt and papper. Process until smooth. You should end up with about 1 cup of the pesto. It will have a saucelike consistency.

Plae half of the pesto in a large bowl, add the shrimp, toss and coat thorougly.

Prepeare a medium-hot grill. Grill the shrimp for 2 minutes; using tongs, turn and grill the other side for another 2 minutes. Transfer the cooked shrimp to a platter and drizzle with the remaining pesto. Serve warm or at room temperature.