Roast lamb and mint is the cold roast lamb sandwich resolved with mint, and the mint is the part that makes it work. Cold roast lamb is a strong, slightly sweet meat with a distinctive fat that firms as it cools and, left to itself between bread, sits heavy and insistent on the palate, one rich register the whole way through. A spread of fresh mint sauce, sharp with vinegar and edged with sugar, or mint jelly in its sweeter, set form, cuts straight across that lamb fat with acid and a clean herb note at once. This is the defining pairing rather than seasoning laid on top: the mint is the part that tells you which roast you are eating and does the work the gravy and the mint sauce did together on the Sunday plate.
The craft is in the slicing and the measure of the sauce. Cold roast lamb is best cut thin and against the grain, because a thick cold slice is chewy and emphasises the firmed fat, while a thin one stays tender and folds to the bread. Mint sauce is wet and sharp, so it goes on in a measured stripe and the lamb is laid as a partial barrier between it and at least one face of the loaf, since a flood of vinegary sauce soaks through to a sour patch within minutes. Mint jelly behaves differently, set and sweeter, so it spreads without bleeding but pushes the balance toward sweet against the meat. The bread needs structure for a dense filling, a sturdy white or a bloomer, and butter to the edges seals the crumb against the sauce and bridges the salt of the lamb to the wheat.
The variations are mostly a question of the mint's form and a few related cuts. Fresh vinegar mint sauce keeps it sharpest; mint jelly turns it sweeter and rounder; a stripe of redcurrant alongside pushes it toward the fruited counter lamb also takes well. The same lamb without the mint is a plainer cold-roast reading, and a hot lamb roll with gravy belongs to its own tradition. Each deserves its own article rather than being crowded in here.