Heat gas or charcoal grill to medium- high at least 30 minutes.

Cut pickles, onion, and bread into 1-inch chunks.

Form beef into 12 small patties, roughly the same size as pickles, onions, bread, and tomatoes. Skewer a bread piece, 2 beef patties, pickle, red onion, tomato, and another bread piece; repeat to create 2 deconstructed burgers per skewer. Repeat with remaining ingredients and skewers. Drizzle with olive oil and sprinkle with salt and pepper on all sides.

Place skewers on grill, and cook until ingredients start to brown, moving skewers to a cooler part of the grill if bread chars too quickly, about 6 to 8 minutes for medium-rare or 1 to 2 minutes longer for medium to medium-well. Sprinkle grated cheese on meat (or everything, if you like) during final minute of cooking, and close grill to melt fully. Remove skewers from grill, and serve warm.