In a small pot over medium-high heat, place the vinegar and sugar; heat to a low boil to dissolve sugar into the vinegar. Turn off heat and stir in the mint.
Combine chopped cucumber, onion and red pepper in a bowl, and pour hot vinegar over the top. Stir to combine and let stand, stirring occasionally.
In a large mixing bowl, combine the ground meat with the tamari, peanut butter, garlic, ginger, chives and black pepper. Form an even mound of meat, score it into 4 equal portions and from each portion form 2 patties, about 3 inches in diameter each.
Heat vegetable oil in a cast-iron or nonstick skillet over medium-high to high heat. Add the patties and cook 3-4 minutes on each side, until golden and firm.
To serve, place a little shredded cabbage on the bun bottoms, top with the patties, some cucumber relish and the bun tops.