Pickled Cucumbers:

In a bowl, stir together vinegar and sugar until sugar is dissolved. If using ginger, chop. 

Slice enough cucumber crosswise into 1/8 inch-thick slices to measure 1 1/2 cups and add to vinegar with ginger, tossing well.

Marinate mixture at least 30 minutes and up to 4 hours.

Burgers:

Prepare grill. Mince garlic.

In a blender, tear bread slices and grind into fine crumbs. 

In a bowl,  mix garlic with bread crumbs  and remaining burger ingredients with your hands until just combined (do not overmix). Form into four 1-inch-thick patties.

Season burgers with salt and pepper and grill on a lightly oiled rack set 5 to 6 inches over glowing coals about 5 minutes on each side, or until just cooked through.

Transfer burgers to buns and top with drained cucumbers.

This recipe can be prepared in 45 minutes or less but tastes like you took all day.