Preheat your oven to 400F and line a baking sheet with parchment or foil.
To make the marinade, whisk the vinegar, oil, liquid aminos, maple syrup, smoked paprika, and cayenne, if using, together in a small mixing bowl.
Place the carrots onto the parchment. Pour about 1/3 of the marinade over them, then toss the carrots with your hands to coat them evenly. Place the baking sheet into the oven and roast the carrots for 20 minutes. After 20 minutes, use a basting brush to brush another few tablespoons of the marinade over the carrots (or pour another third of the marinade over the carrots and use the basting brush to spread it around). Repeat this after 40 minutes. After 50-60 minutes, or when the carrots are browning, shriveling, and very tender, remove them from the oven.
While the carrots roast, make the delightfully green tahini dressing or any other sauce you'd like to serve with them.
Once the carrots have finished roasting, reduce the oven heat to 300F. Place the hot dog buns on another baking sheet and bake for 10 minutes, or until they're lightly toasted.
To serve, place one roasted carrot in each bun, drizzle with sauce, and enjoy.