Mix sugar and brown rice vinegar in a bowl. Either let sit or whisk until sugar dissolves. You can also heat the brown rice vinegar until it is warm and pour over sugar to dissolve. Once the sugar is dissolved, add julienned carrot. Let marinate in the fridge at least 2 hours.
Mix sriracha, vegan mayo, and lime juice.
Cook hot dogs per instructions. Slice the buns, heat in the microwave for 15-30 seconds, and hollow out a little of the bread.
Splash a little tamari into each bun. Spread sriracha mayo sauce on buns and pile in hot dogs, cucumber slices, pickled carrot, serrano pepper, and cilantro. Squeeze lime juice on hot dogs and serve.