Using a peeler, peel the carrots, taking care to round the two ends and even make a few star-shaped notches (we want them to look like hot dogs/sausages as much as possible).
In an oven-safe bowl add the broth, cider, soy sauce, maple syrup, liquid smoke, paprika powder and garlic powder. Mix well and then add the carrot.
Marinate for 2 hours.
Preheat the oven to 400 ˚F.
Place the bowl with carrots and marinade in the oven and cook covered for 40 minutes, uncover and cook for another 20 minutes.
Toast the buns.
Put a carrot in each bun and the condiments of your choice.