The white pudding sandwich is defined by what it leaves out. White pudding is the bloodless relative of black pudding: oatmeal, pork, fat, and seasoning packed into a skin and sliced, with none of the blood that gives black pudding its dark colour and metallic depth. The result is milder, paler, and oat-forward, the cereal and the soft pork fat carrying the flavour rather than iron, and the sandwich is built around exactly that gentler register. Fry the slices until the cut faces crisp and the oatmeal inside goes soft, lay them on a buttered roll or soft bread, and the defining note is savoury, peppery, and rounded rather than rich and dark.
The craft is the fry and the carrier. White pudding holds together loosely once heated, so the slices are cut a decent thickness and fried hard enough to set a crisp shell on each face, which is what stops the filling collapsing into crumbs between the bread. The roll is soft and slightly absorbent so it takes a little of the rendered fat without disintegrating, and butter on the bread bridges the salt of the seasoning to the wheat. Brown sauce is the usual condiment, applied inside in a measured stripe so it sharpens the soft, oaty fat without running, since a flood of sauce would turn an already gentle filling shapeless.
The variations sit inside the cooked-breakfast frame. A fried egg adds a yolk the bread then has to manage; bacon alongside brings a salt-and-crisp counter the pudding lacks on its own; black pudding is the close, blood-rich cousin that runs the same fry-and-roll logic with a darker, more mineral filling. Each deserves its own article rather than being crowded in here.