Pre heat oven to 220˚ C (200° C fan forced). In a bowl combine vegetable stock, vinegar, soy sauce, honey, smoked paprika, and garlic. Whisk until ingredients are evenly distributed. Place carrots in an appropriately sized baking pan and pour stock mixture over top, carrots should not be submerged. Allow to marinate 30 minutes - 1 hour, tossing occasionally.
Cover pan with foil and roast carrots for 30 minutes. Remove foil and turn carrots to coat in marinade. Return to oven and continue cooking until tender. Keep warm until ready to serve.
Set grill to high. Place carrot "hot dogs" on grill to mark and toast buns.
To serve place grilled carrot in toasted bun and top with 1 tablespoon caramelized onions and finish with a drizzle of Yellow Mustard and generous serving of charred tomato ketchup.
Carrot hot dogs can be cool and reheated as needed.