The chip cob is the chip butty under the East Midlands word for its bread, and the word is not a trivial detail. Across Nottingham, Derby and the surrounding towns the soft round roll that everywhere else is a bap, a barm, a batch or a bun is a cob, and ordering chips in a cob rather than chips in a barm tells a chippy where you are from before it tells them what you want. The defining fact of this build is therefore the bread format itself: not two slices of a folded loaf but a single round roll, split, buttered and packed with hot chips, which makes a denser, rounder, more enclosed sandwich than the flat butty.
The craft is the cob holding a loose, hot filling without going to mush. A cob has a firmer crumb and a thin, slightly chewy crust where the flat white loaf of a butty has neither, and that structure earns its keep here: it takes the weight and steam of a fistful of just-fried chips and stays a sandwich rather than collapsing into a damp parcel. The split roll is buttered on both cut faces so the fat melts into the chips and meets them from above and below, and so the crumb is sealed against the steam coming off them. Chips go in hot enough to soften the butter on contact, that fat-and-potato slick being the only sauce a plain chip cob has, and they are pressed down so the roll closes around them and binds the loose chips into something that holds for the walk. Brown sauce or ketchup goes inside as a stripe, never a flood, because the cob's crumb is more absorbent than it looks and a pool would soak straight through the base before the roll was finished.
The variations are the same chip-in-bread idea under the rest of the regional bread map and the chippy condiment rack. Chip barm, chip butty, chip bap and chip batch are the same sandwich wearing other towns' words. Curry sauce, gravy or mushy peas turn the dry cob into a wet meal; cheese melted into the chips makes the loaded version, and a chip cob with a fish finger or two added pushes it toward a chip-shop butty. Each deserves its own article rather than being crowded in here.