The egg and chips sandwich takes a complete cafe meal and folds it into bread, and its whole argument is that yolk and chips are themselves a sauce-and-carbohydrate pairing that needs nothing else. Egg and chips on a plate is eaten by dragging the chips through a broken yolk; this sandwich fixes that gesture in place. A fried egg goes on soft buttered bread with a handful of hot chips, the bread is folded over and pressed, and the yolk becomes the dressing that binds the loose chips into the loaf. There is no protein logic beyond the egg and no pretence of balance. It is carbohydrate on carbohydrate with a rich yolk doing the work a condiment would do in any other sandwich.
The craft is the yolk decision and the press. The chips have to go in hot so they keep some crisp against the soft bread for as long as possible, and the egg is the variable that defines the build: a soft yolk runs through the chips and the crumb as a sauce, which is the point of the sandwich but also why it has to be eaten at once, while a firmer yolk holds together and travels but gives up the binding flood that justifies the whole thing. The bread is deliberately soft and plain so it yields to a lumpy, uneven filling rather than fighting it, buttered to the edge so it does not soak straight to paste, and the press is what turns loose chips and a sliding egg into something that holds for a few bites.
The variations push the same carb-and-yolk idea rather than away from it. A stripe of brown sauce or ketchup adds the acid the build otherwise lacks; mushy peas turn it into a fuller chip-shop meal in the hand; a second egg or a thicker cut of chip changes the ratio without changing the principle. Those deserve their own articles rather than being crowded in here.