Step 1

In a large enameled cast-iron casserole, heat the oil until shimmering. Add the onions and cook over moderate heat, stirring occasionally, until the onions are wilted and just starting to brown, about 7 minutes. Add a generous pinch of salt and cook over moderately low heat, stirring occasionally, until the onions are soft and golden, 25 to 30 minutes.

Step 2

Add the wine and soy sauce to the casserole and cook over moderate heat, scraping up any browned bits from the bottom, until evaporated, about 3 minutes. Add the stock and bring to a boil. Simmer over moderately low heat, stirring occasionally, until the broth is well flavored and slightly reduced, about 10 minutes. Season the soup with salt.

Step 3

Meanwhile, preheat the broiler. Arrange the bread on a baking sheet and top each piece with 1 tablespoon of the cheese. Broil 6 inches from the heat until the cheese is melted and just starting to brown, about 2 minutes. To serve, ladle the soup into bowls and top with the toast.