PREP - Heat grill. Brush the eggplant slices with olive oil and season both sides. Sprinkle BBQ rub and a little olive oil over both sides of the steak. Butter both sides of 4 bread slices.
PRE-COOK - Grill the steak over a hot fire for 2-3 minutes on each side. Lower heat to medium and grill the eggplants. In a frying pan over medium heat, crisp bacon and then fry eggs on both sides. Toast both sides of unbuttered bread slices on the grill or in a toaster. Slice steak into thin strips.
ASSEMBLE - Lay 2 slices of butter bread on a board. Layer each in the following order: bacon slices, an egg, steak slices, eggplant slices, salt, and pepper. Top with 1 toasted slice and then layer with tomato, salt, pepper, cheese, and onion. Top everything with a remaining slice of buttered bread. Tie sandwich like a parcel with kitchen twine to hold everything together when grilling..
FINISH - Toast sandwiches on the grill over low heat until the cheese melts and the bread becomes golden brown, about 5 minutes per side. Remove string, cut in half diagonally, serve.