The Jersey breakfast sandwich is a regional argument about one ingredient, and the ingredient is the cured pork. Egg and cheese on a roll is a national baseline; what makes this version a New Jersey sandwich is that the meat is Taylor ham, the state's particular pork roll, sliced thick and griddled so it lies flat. The defining move is in the prep of that disc. Pork roll cups violently on a hot griddle unless the edges are scored, four cuts to the rim, so it stays flat and takes an even sear instead of curling into a bowl that cooks unevenly and rocks on the bread. That scored, flattened disc of salty cured pork is the whole identity; the egg and cheese are the constants around it.
The craft is in the carrier and the build order. The roll is a hard kaiser-style roll, a crust with structure and a tender crumb, chosen because it has to take a hot, fatty, one-handed load without going to paste before the eater reaches the car. The egg is cooked to stay soft and folded to the size of the roll so it acts as both filling and binder, gluing the cheese and the pork into a single mass rather than a stack that slides apart on the first bite. American cheese is laid on while everything is still hot so it melts into the egg and seals the structure. Hash browns, when added, go in as a flat pressed layer for crunch, not a loose handful that breaks the seal. Assembled fast, wrapped in foil, the thing arrives structurally sound and hot, which is the entire brief.
The variations are mostly the order argument the state runs on. The build is identical whether it is called Taylor ham or pork roll, and the disagreement over the name is itself the regional signature. Pepper, egg, and cheese drops the pork entirely; a bacon or sausage reading swaps the cured meat and changes the sandwich. The carrier moves from the hard roll to a bagel for a heavier load or a bialy for a softer one. Each of those is its own codified build with its own defenders, and each deserves its own article rather than being crowded in here.