A garlic emulsion does more than season this sandwich: it is the binder that holds the whole thing together. Aïoli is the Provençal sauce of raw garlic pounded to a paste and emulsified with olive oil into something thick, glossy, and pungent, closer to a stiff mayonnaise than to a dressing. In the sandwich it is spread heavily on a split crusted loaf, and the filling is built into it: usually cooked vegetables and a hard-boiled egg, sometimes flaked white fish, the components the sauce traditionally accompanies on the plate, here packed into bread.
The logic is that the sauce carries everything. Aïoli is rich with oil and sharp with raw garlic, so it coats mild vegetables and binds them to the bread the way a dressing binds a salad, no other condiment needed. The constraint is the garlic: it is forceful and it does not fade, so the rest of the sandwich stays gentle, boiled potato, green beans, carrot, egg, things that give the sauce something soft to hold without competing with it. The oil in the emulsion soaks the crumb, so the loaf needs a crust firm enough to survive being saturated from the inside. This is a sandwich that eats cool and dense, the garlic building rather than receding as you go, which is the point rather than a flaw; it is closest in spirit to the grand aïoli, the Provençal spread of vegetables and sauce, compressed into a portable form.
Variations move within the same plate of food. A version with flaked salt cod adds a saline note the vegetables lack; one heavier on egg and potato is milder and more filling; a lighter build with raw crudités keeps the vegetables crisp against the soft sauce. Each holds the garlic emulsion as the fixed point and changes what it binds. The Sandwich à l'Aïoli sits with the plant-forward sandwiches the catalog groups under Sandwich Végétarien, the tradition that builds a sandwich from vegetables and a strong dressing rather than from cured meat. Its specific contribution is a sauce assertive enough to be the structure, so the cook's only real decision is what mild thing to suspend in it.