The kedgeree sandwich takes a dish that is already a finished, multi-component breakfast and asks bread to contain it, which is the whole problem and the whole interest. Kedgeree is flaked smoked haddock, curry-spiced rice, and chopped hard-boiled egg, an Anglo-Indian breakfast eaten warm with a fork. Pressed between slices it becomes a sandwich whose filling is loose, granular, oily from the fish, and laced with spice, none of which a slice naturally wants to hold. The defining decision is therefore not what goes in but how the filling is brought under control before it ever meets the bread. Get the moisture and the bind right and it works; treat it like a wet stew and it collapses into the crumb.
The craft is drying the filling and managing the spice. The rice is the structural element: cooked dry and cooled so it is a binding bed rather than a slick, it holds the flaked haddock and the chopped egg in place the way a tight bound filling holds in any sandwich. The smoked haddock is flaked fine and well drained so its oil does not pool and soak through, and the egg is chopped rather than mashed so it adds body without turning the whole thing to paste. The curry spice is calibrated against that fixed mass: enough to read as the warm, mild kedgeree note, not so much that it overwhelms a filling with no cooling element built in. The bread is plain and soft and buttered to the edges, the butter sealing the crumb against an oily filling, and the load is kept moderate because an overfilled kedgeree sandwich simply spills its rice the moment it is bitten.
The variations track the breakfast dish more than the sandwich. A version bound with a little mayonnaise or crème fraîche turns the loose rice into something closer to a salad filling that holds better cold. The smoked haddock sandwich on its own, without the rice and egg, is the cleaner coastal build the kedgeree is elaborated from. Each of those deserves its own article rather than being crowded in here.