Young carrots are best for grilling, as they're more tender, less dense and cook quickly. Small, thin carrots can be grilled whole. Older, larger carrots can be cut on a diagonal into thick slices. This helps expose more surface area to the heat. You can also cut carrots in half lengthwise before grilling for the same effect. To speed up cooking time, you can blanch the carrots for 2 to 3 minutes before placing them on the grill.