To make the herb pesto: add the parsley and tarragon to a mini food processor or blender and pulse to a rough chop. With the motor running, slowly drizzle in the olive oil. Add a pinch of salt and season to taste. Set aside while you grill the carrots.
Preheat the grill to 500°F. Scrub or peel the carrots and brush with olive oil. When the girl is at temp, add the carrots to the grill.
Turn the carrots every few minutes until they are evenly charred on all sides. This should take 15-20 minutes depending on how thick they are.
Remove from the grill and arrange on a platter. Drizzle with the pesto and serve the extra sauce on the side.