Trim the lengths of the peeled carrots to fit a hot dog bun.
In a bowl, mix together the marinade - vegetable broth, soy sauce, apple cider vinegar, maple syrup, mustard, garlic powder, onion powder, smoked paprika, and black pepper.
Quicker Method
Add the carrots and the marinade to a saucepan (one wide enough so the carrots can lay flat.)
On medium heat, bring to a boil. Reduce to low and let simmer for about 10-12 minutes, covered, or until the carrots are just fork-tender.
Remove from the heat and let the carrots marinate in the liquid for at least 30 minutes, turning halfway through.
Overnight Method
Follow the Quicker Method steps 1-2.
Transfer the carrots and hot marinade (very carefully) to a storage container. I typically remove the carrots first, then pour the liquid over the carrots, to reduce splash. You don't need to add ALL of the liquid if it won't fit in the container. Just enough to cover the carrots.
Store in the fridge overnight. To reheat the next day, warm up in a skillet with a little oil, grill them, or put them in a microwave.
Instant Pot
Add the carrots and marinade to the Instant Pot. Set to high pressure on manual for 3 minutes. Make sure the valve is set to sealing.
Quick Release the pressure when the timer goes off.
Let sit in the liquid for about 10 minutes before removing.
Grill (Optional)
This is an optional step after cooking the carrots using one of the 3 above methods.
On a grill set to high heat (outdoor or stovetop grill pan), grill for about 1 minute on each side, or until the carrot dogs are charred to your preference.
Add to a bun with your favorite toppings and enjoy!