- Trim carrot tops from carrots and set aside. Scrub carrots under running water and set aside. Fill a medium bowl with water. Pluck carrot top leaves from stalk and drop into water. Pluck parsley leaves and add them to bowl of water with carrot top leaves. Set carrot top stalks and parsley stems aside for a future vegetable stock or discard into compost bin. Place carrot and parsley leaves in a salad spinner and spin dry, or set in a colander to drain and wrap in paper towel to dry.
- Preheat grill to 500 degrees. On a cutting board, thinly slice scallion crosswise. Place scallion in a small bowl. Peel and halve shallot. Finely dice the shallot and add to bowl with scallion. Rub clove of garlic across a Microplane zester over bowl with the scallion and shallot. Finely chop anchovy and add to bowl. Reserve 1 tablespoon of olive oil for carrots, then stir in remaining oil into herb mixture and set aside.
- Place carrots in a wide dish, such as a shallow casserole. Drizzle reserved oil onto carrots, then season with salt and pepper. Transfer carrots to hot grill and place them crosswise against openings between grates. Let cook until charred on one side, about 3 minutes, then turn and repeat until a nice char forms on all sides of each carrot. Return carrots to the dish and let cool slightly, then transfer them to the cutting board and cut them into 2-inch-long pieces on a bias. Place sliced carrots on a serving plate or platter and spoon the salsa verde over the warm carrots. Can be served warm or at room temperature.