Adding cheese to a French dip is not a garnish decision; it rewrites how the dip works. The plain French dip is a control problem: thin-sliced roast beef on a French roll with the jus served in a cup so the eater decides, dunk by dunk, how wet the sandwich gets. Lay a slice of melted Swiss or American between the beef and the top of the roll and that calculation changes, because the cheese is a partial moisture barrier. It seals the upper crumb against saturation, so the same dunk wets the bottom of the sandwich and the meat while the cheesed side stays comparatively intact. The eater is still working the dry-versus-soaked dial, but the cheese moves the dial's range and slows how fast a dunk travels through the bread.
The craft is in what the cheese adds and what it costs. Roast beef and its jus are lean by design, so the fat a melted slice brings is not redundant the way it can feel on a richer sandwich; it rounds a stock that is otherwise all savory and salt, and it clings to the beef where the jus runs off. Swiss melts smooth and nutty and reads against the jus without fighting it; American slumps and seals more completely, leaning the build toward coating rather than flavor. The trade is structural. Cheese binds the stack so the sliced beef stops sliding out under the dunk, but a cheese-sealed roll absorbs jus unevenly, soaking from the cut and the underside rather than wicking through the whole crumb, which means the bread holds up longer but never goes uniformly dark the way an undressed French roll does. The slicing discipline is unchanged: beef cut against the grain as thin as the machine allows, so a forkable pile stays tender when it finally meets liquid. The jus is still the load-bearing flavor and still built to stand on its own from a cup, because it has to season every bite the eater chooses to dip.
The cheesed French dip sits in the wet-roll roast beef family alongside the Chicago Italian beef, which pre-soaks the roll instead of leaving the jus in a cup, Buffalo's beef on weck with its salt-and-caraway roll and horseradish, and the pastrami dip that runs the method over cured beef. Each of those is its own discipline and deserves its own article rather than being crowded in here.