The ham here does not arrive as a slice at all; it arrives as a terrine, set in jelly and cut from a block. Jambon persillé is a Burgundian preparation, the region it belongs to: cooked ham broken into coarse pieces, packed into a mold with a wine-and-herb stock heavily flecked with parsley, and set into a jelly so it slices as a marbled block of pink meat, green herb, and clear aspic. The components are a fresh baguette, a layer of barely-salted butter, and a thick slice of that set terrine. The defining element is not the meat alone but the parsleyed jelly that binds it, which behaves on the sandwich very differently from a simple cut of ham.
The craft is in handling something that is meat and set liquid at once. The terrine has to be cut thick, in a slab, because thin slices fall apart along the lines of the jelly and lose the marbled structure that is the whole point. Sliced properly it brings its own moisture and its own acidity from the wine in the aspic, which changes the butter's job: here the butter is less a counterweight to salt than a cushion between the cool, faintly sharp terrine and the wheat of the crust. The bread has to have a firm crust and a sturdy crumb, because the filling is soft, wet, and heavy, and a slack loaf would collapse under it. This is a sandwich eaten cool and unhurried, and it is best within a short window of assembly, before the aspic warms and softens against the bread. No cornichon is needed: the acidity is built into the terrine.
Variations are the broader French ham shelf rather than mutations of the terrine itself: a pale boiled slice, a dry-cured leg, a mountain ham, each taking the form somewhere firmer and drier. Those carry their own qualifiers and their own articles rather than being crowded in here. This is the most transformed member of the family that orbits the canonical Jambon-Beurre: the same baguette and butter, but the ham rebuilt into a Burgundian parsleyed terrine, and the jelly doing the work the slice cannot.