Heat the olive oil in a large skillet over high heat. Add the garlic and cook briefly to release its fragrance. Add the onions and a little salt to help the onions release their liquid. Cook briskly, stirring often, for about 7 minutes, then reduce the heat to moderate and cook, stirring occasionally, until the onions are golden brown, about 25 minutes more.

Add the sage and vinegar and cook until the liquid evaporates. Add the stock and simmer for 10 minutes.

Preheat the broiler. Transfer the soup to a flameproof serving dish. Bring the soup to a boil on top of the stove. Top with the croutons, then with the Fontina. Broil until the cheese melts, then serve immediately.