Trim off the ends of the onions. Cut each onion in half lengthwise. With a very sharp knife, cut the onions into paper-thin slices and place in a shallow, non-reactive dish, such as a glass pie plate. In a medium bowl combine the remaining onion ingredients. Whisk thoroughly to dissolve the sugar and salt. Pour the vinegar mixture over the onions and stir to coat them evenly. Set aside at room temperature for about 3 hours, stirring the onions occasionally. Drain the pickled onions and set aside.
Using a sharp knife, cut a few shallow slashes in each hot dog.
Prepare the grill for direct cooking over medium heat (350° to 450°F).
Brush the cooking grates clean. Grill the hot dogs over direct medium heat, with the lid closed as much as possible, until lightly marked on the outside and hot all the way to the center, 5 to 7 minutes, turning occasionally.
Place the hot dogs in buns. Squeeze your condiment of choice alongside each hot dog and top with pickled onions. Serve warm.