Wash and peel carrots. Cut until they're hot dog length and uniform in width.
Place carrots in boiling water. Boil for 5-10 minutes until just fork tender.
Drain carrots, rinse with cold water, and drain again.
Whisk together all the marinade ingredients and pour into a container with a tight fitting lid that's big enough to fit the carrots.
Place carrots into the container. Close the lid and shake until the marinade has covered the carrots.
Marinate for at least 4 hrs, preferably overnight. Shake a few times while marinading. Save marinade.
After carrots are marinated, heat an indoor or outdoor grill over medium high. Once water droplets sizzle on the grill, add the carrots, insuring they aren't touching.
Grill carrots on an open grill, turning and basting, until they have have grills marks on both sides, about 5-15 minutes.
While carrots are grilling, preheat oven to 350° Fahrenheit. Oil an 8x8 baking dish and add a little marinade to cover the bottom.
Place grilled carrots in the baking dish and brush them with more of the marinade.
Bake until carrots are a meaty consistency about 20- 50 minutes. Turn once after 10 minutes and baste with more marinade.
Remove carrots from oven and serve on hot dogs buns.