The bacon, egg, and cheese is engineered around a hot egg, and the egg sets every other decision in the sandwich. Cooked on a flat-top griddle and kept soft, folded or broken to roughly the footprint of the roll, it is the filling and the binder at once: the American cheese is laid on the egg while it is still on the griddle so it melts into it, and that molten layer glues the bacon and the egg into a single mass that survives being wrapped in foil and eaten one-handed on a sidewalk. Speed and portability are the entire design brief, and the egg is what makes the build cohere rather than fall into its parts.
The craft is in the griddle and the carrier. The bacon is cooked crisp because it is the only firm, salty texture in an otherwise soft sandwich; gone limp, it disappears into the egg and the build loses its spine. The cheese is melted onto the egg rather than laid on cold, which is the small move that turns three ingredients into one structural object instead of a stack. The roll is the bodega kaiser or a hero, soft-crumbed but sturdy enough to take the grease without going to paste, split and often griddled on the cut faces so it has a little structure against a wet filling. Salt, pepper, and for many orders a squirt of ketchup or hot sauce go in before it is wrapped, because the foil steams the whole thing into a sealed, structurally sound unit on the walk. It is made in under a minute, to order, on a griddle that never cools, which is exactly why it works.
The variations are mostly a swap of the cured pork on the same frame. Sausage or ham stands in for bacon; the roll becomes a bagel when a chewier carrier is wanted, or a hard roll, or a wrap. New Jersey runs the same build on griddled pork roll instead of bacon, and the Southern reading moves it onto a split biscuit. Each of those regional readings deserves its own article rather than being crowded in here.