1. Begin by bringing a pot of water to a rolling boil.
2. While the water heats up, prepare your carrots by cutting them to fit the size of your hot dog buns. Trim any excessively thick ends to maintain uniformity.
3. Once the water is boiling, carefully add the carrots and let them simmer for 10-15 minutes until they reach a slightly tender consistency. Test them with a fork—they should offer some resistance but still be penetrable.
4. Meanwhile, in a mixing bowl, combine all the ingredients for the marinade, whisking until well blended. Transfer the marinade into a large freezer bag.
5. Once the carrots are done, drain them and rinse under cool water to halt the cooking process. Then, place them into the freezer bag with the marinade, ensuring they're well coated. Seal the bag and gently massage to distribute the marinade evenly.
6. Refrigerate the bag for 4-6 hours to allow the carrots to absorb the flavors. If preparing in advance, after the 6-hour mark, transfer the carrots into an airtight container. Reserve some of the marinade in a separate container.
7. Prior to grilling, preheat and grease a grill pan over the stove or fire up the barbecue.
8. Remove the marinated carrots from the fridge and set aside some of the marinade with a brush. Grill them on all sides until they're thoroughly cooked and bear distinct grill marks. While grilling, periodically brush them with the remaining marinade for extra flavor.
9. Once grilled to perfection, your carrot dogs are ready! Serve them with your preferred toppings and enjoy this veggie twist on a classic favorite.