Make the tahini sauce: whisk all sauce ingredients in a medium bowl, adding enough water to achieve the desired consistency. This will depend on the consistency of the tahini. Figure about 1/3 cup of water, more or less.
Prepare a charcoal grill for direct, high heat grilling or heat a gas grill to high. (Alternatively, heat a cast-iron grill pan over high heat.) Scrub the carrots clean and dry thoroughly, then place in a bowl or on a baking sheet. Toss to coat the carrots with the oil and season them with salt and pepper.
Place the carrots on the grill and cook, turning as they char lightly, until soft and blackened nicely in spots, about 20 minutes for large carrots or 10 minutes for small, thin carrots.
While the carrots cook, spread some tahini sauce over the bottom of a large serving platter. Transfer the cooked carrots directly from the grill to the platter, piling them up in the center. Sprinkle a little vinegar on and around the carrots. Garnish the carrots with any of the optional finishing ingredients, if desired. Just wing it with amounts. Serve the extra tahini sauce on the side.