The Stornoway black pudding sandwich is named for a specific pudding from a specific place, and that specificity is the point of it. Stornoway black pudding is made on the Isle of Lewis in the Outer Hebrides and carries a protected geographical status, which fixes both where it is made and roughly how: a firm, dark, oat-heavy pudding, less rich and less fatty than many mainland versions, with a dry crumbling set rather than a soft greasy one. The defining fact of the sandwich is that the named pudding does its own structural and seasoning work. Where a generic black pudding leans wet and needs managing, the Stornoway block is dense and peppery and holds a sliced shape, so the build can stay simple and let the pudding be the whole statement rather than a thing to be rescued.
The craft is the cooking of the slice and the restraint of everything around it. The pudding is cut into rounds and fried or griddled until the cut faces crisp and the oat-bound interior heats through to a crumbly, savoury set, because Stornoway pudding browns and firms rather than melting into the pan the way a fattier one does. It goes hot into a soft morning roll or a floured bap chosen to take a little of the rendered fat without disintegrating, the bread doing the absorbent-carrier job it does across the breakfast shelf. Butter on the roll bridges the salt of the pudding to the wheat; a sauce, brown or red, is applied inside in a measured stripe so it seasons without flooding a filling that is already well spiced. The pudding carries enough pepper and salt of its own that nothing more is needed, which is the locality showing through in the build.
The variations stay inside the breakfast-roll frame and mostly add a single counter to the same Hebridean constant. A fried egg lays a soft yolk over the crumbling pudding and binds the roll. A rasher of bacon doubles the salt and the savour. A tattie scone slid in alongside turns it into a fuller Scottish breakfast in one hand, and the stack with neeps or with white pudding pushes it toward the plate it came from. Each deserves its own article rather than being crowded in here.