In a small sauce pan, combine the vinegar, water, brown sugar, mustard, salt, pepper and celery seed.
Heat to a low boil, stirring frequently, until the sugar has dissolved.
Place the cabbage slaw mix in a medium sized bowl. Pour the hot vinegar mixture over the vegetables. Stir to coat well. Chill while preparing the burgers and buns.
Prepare the hamburger patties to package instructions for grilled. Spread the butter on the inside of each bun, and lightly toast them on the grill.
Assemble each burger with a bottom bun, slice of tomato, dill pickle slices, hamburger, and top with a generous amount of the vinegar slaw. Top with a bun and serve warm.