The scrambled egg and smoked salmon sandwich is led by the salmon, and the egg is the soft bed it sits on. Cold-smoked salmon is silky, salty, and oily, with a cure that carries its own concentrated savour, and in this sandwich it is the loud component: a soft, slow-cooked scramble is piled into bread and draped or folded through with ribbons of the salmon. The eggs are deliberately mild and rich so they do not compete; their job is to be a warm, creamy carrier that lets the salmon read clearly. This is the brunch register of the British egg sandwich rather than the lunchbox one, and the defining fact is the pairing of a cool, cured, salty fish against warm, loose, gentle egg, two soft things set deliberately at different temperatures and intensities so each is felt against the other.
The craft is restraint and moisture control on two fronts. The scramble is taken off the heat underdone because it sets further in its own warmth, and it is kept loose rather than dried out, which means it carries free moisture that the bread has to be defended from. The salmon is added at the end, off the heat, because cooking it tightens it and dulls the smoke; it goes in as ribbons folded through the warm egg so the egg's heat just softens it without cooking it. Butter to the edges waterproofs the crumb against the scramble's moisture and the salmon's oil. The bread is restrained, soft white or a thin brown, because the salmon is already salty and assertive and a heavy loaf would crowd it; the salt of the cure means the build needs almost no extra seasoning beyond pepper and perhaps a squeeze of lemon. It is eaten promptly, before the egg soaks through.
The variations stay in the same soft, cured frame. A little dill or chive cuts the richness; cream cheese in place of, or alongside, the egg is the bagel reading of the same pairing; the salmon on plain buttered brown bread without the egg is the afternoon-tea version, stripped to fish and bread. The wider egg sandwiches and the smoked-fish builds are the same components met apart rather than together. Each of those deserves its own article rather than being crowded in here.