Ham and pease pudding is a Northeast sandwich, and the pease pudding is the part that makes it itself. Pease pudding is a thick, smooth purée of dried split peas, cooked down soft and seasoned, dense enough to spread and hold its shape rather than run. Against cooked ham it is not a sauce and not a pickle; it is a starchy, earthy, mildly sweet legume paste that does a job neither butter nor mustard does. It adds body and a soft, almost nutty counter to the salt of the meat, and it binds the sandwich into one substance instead of two layers. The defining move here is the legume against the cured pork, a pairing of pease and ham that the Northeast has kept when the rest of the country largely let pease pudding go.
The craft is the spread and the moisture, and pease pudding solves more than it creates. It is cooked thick on purpose so it can be spread like a paste and will sit in a layer without bleeding into the crumb, which makes it kinder to bread than a wet pickle or a running egg. It goes on generously, because the whole point is body, and the ham, cold and salty, is laid against it so the two read in the same bite rather than as a stripe of one and a slab of the other. Butter still goes to the edges underneath, bridging the salt and sealing the crumb. The bread is soft and plain in the everyday form because the filling is dense and mild and wants a yielding carrier, not a chewy one that competes with a paste that has no texture of its own.
The variations are mostly the bread under the same pairing. Put ham and pease pudding in a stottie, the dense Newcastle griddle bread, and the loaf becomes the headline. A saveloy and pease pudding swaps the cured ham for a fried red sausage and keeps the paste; a bacon and pease pudding shifts the cure again. Each of those is its own sandwich and deserves its own article rather than being crowded in here.