Boil water in a pot large enough for all the carrots. Lower the heat to medium and add the carrots. Cook until just fork-tender when you bite into them. Remove from pot and run under cold water.—you want them to have a snap
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 3-4 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 1/8 cup. If the carrots are very thin, keep the time short.
To serve, put the carrots in a 350 F oven, or in a grill pan on a hot grill, until heated through, 10-15 minutes. You can also cook these in your slow cooker in the marinade. You need to check on them so they do not get mushy, so it is not a set-it-and-walk-away affair. Cook until a fork just goes through the carrot but it is still slightly firm.
Serve in a toasted hot dog bun or wrapped in a lettuce or collard leaf, and pile on your favorite toppings, including mustard, relish, tomatoes, onions, sprouts, purple cabbage, and peppers.