Add the carrots to a small roasting pan and toss with olive oil. In a small bowl, whisk together broth, vinegar, soy sauce, maple syrup, garlic powder, paprika and liquid smoke. Pour over carrots and cover pan with foil. Let sit for 30 minutes.
Preheat oven to 425°. Place the foil-covered baking dish in the oven and roast carrots for 30 minutes. Remove the foil and roast for another 20 minutes, until the carrots are just tender enough to stab with a fork.
Place carrots in hot dug buns, serve with ketchup, mustard, and onions.
Personally, this wasn’t my favorite recipe but I think it has potential. The flavor is nice but I might add other toppings to enhance the dog. I might try a Chicago style topping next time! Also my buns were really thick (insert sir mix a lot song) so I’d opt for a smaller bun next time.