Mince garlic. Into a blender tear bread slices and grind into fine crumbs. In a bowl with your hands mix garlic with bread crumbs and remaining burger ingredients until just combined (do not overmix) and 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.