Pull the soft boiled ham out of the standard build, drop in a dry-cured leg from the southwest, and the whole balance shifts. Jambon de Bayonne is a pork leg rubbed with salt, often seasoned with the local red pepper, and air-dried over a long maturation in the climate of the Pays Basque, the region it is named for. It comes out deep red, firm, faintly sweet, and concentrated in a way poached ham never is. The components are spare: a fresh baguette, a thick layer of barely-salted butter, and very thin slices of the cured ham. The defining element is the ham's intensity, and the butter is what makes that intensity wearable.
The craft sits in the knife and in the fat. Dry-cured ham is salty and dense, and cut thick it turns chewy while the salt becomes punishing; sliced almost translucent it drapes and yields to the bite, releasing its nuttiness without overwhelming the sandwich. Because curing drives moisture out of the meat, the sandwich brings none of the wetness a boiled ham would, so the butter is doing structural work rather than decoration: spread thick, it cushions the salt, carries the ham's depth, and keeps the crumb from reading as dry. The bread needs a firm crust to stand against the firm meat. A Bayonne ham sandwich tolerates a short wait better than a soft-ham one does, since there is little moisture to soak the crumb, but it is still best within a few minutes of being built, while the butter is cool and the crust still has bite.
Variations follow the dry-cured tradition across the country: a Tarn mountain ham, a generic jambon sec off whatever leg the charcutier has hung, a parsleyed terrine that takes the form somewhere else entirely. Each of those earns its own qualifier and its own article rather than being crowded in here. This sandwich is the dry-cured answer to the canonical Jambon-Beurre: the same baguette and the same butter, with a salt-cured leg standing in for the pale poached one, and the knife and the fat carrying the difference.