Heat water in a pot large enough for all the carrots. When it comes to a boil, turn down to medium heat and add the carrots. Cook until you can just pierce them through with a fork; you want them to have a snap when you bite into them. Remove from pot and run cold water over them to stop them from cooking.
In a container with a tight-fitting lid, combine the remaining ingredients to make the marinade. Tighten the lid and shake until well mixed.
Place the carrots in a container in which they can lie flat. Pour the marinade over them and marinate at least 3 to 4 hours, up to 24. The longer they marinate, the more vinegar flavor they take on. If you know you need to leave them longer than a day, cut the vinegar to ⅛ cup (30 ml). If the carrots are very skinny, keep the marinating time short.
To serve, heat the carrots in a 350°F oven, or in a grill pan on a hot grill, until heated through, 10 to 15 minutes. Serve in a toasted hot dog bun or wrapped in a lettuce or collard leaf, and pile on your favorite toppings.