Directions

1. Heat 2 tablespoons oil in a large Dutch oven over medium-high heat. Add half of the cabbage (about 8 cups) and onion (about 1½ cups); cook, stirring occasionally, until the vegetables are light golden brown, about 15 minutes. Add 1½ tablespoons vinegar; cook, scraping browned bits from the bottom of the pan using a wooden spoon, for 1 minute. Transfer the mixture to a medium heatproof bowl; set aside, uncovered. (Do not wipe the pot clean). Repeat the process with 2 tablespoons oil and the remaining cabbage (about 8 cups), onion (about 1½ cups) and 1½ tablespoons vinegar.
2. Return all of the vegetables to the pot. Add 7½ cups broth, 1 teaspoon each soy sauce, thyme and pepper and ¼ teaspoon salt; bring to a simmer over medium-high heat, stirring occasionally. Reduce heat to medium; cook, stirring occasionally, until the cabbage and onion are tender and the flavors are blended, about 15 minutes.
3. About 5 minutes before serving, preheat oven to broil with rack in middle position. Line a large rimmed baking sheet with foil. Add 5 cups bread and the remaining 2 tablespoons oil; toss until the bread is coated in oil; spread in an even layer. Broil, stirring once, until toasted, about 2 minutes. Push the bread cubes together and sprinkle with ¾ cup cheese; broil until the croutons are crisp and the cheese is melted, about 1 minute. Ladle the soup into 6 bowls; top with croutons. Garnish with additional thyme and pepper, if desired.