Ingredients

• 3/4 stick (6 tablespoons) unsalted butter
• 1 1/2 pound red onions, halved lengthwise, then cut lengthwise into 1/4-inch-thick slices
• 1 (3-pound) head of red cabbage, cut lengthwise into 8 wedges and wedges cut crosswise into 1/4-inch-thick slices (16 cups)
• 2 cups dry red wine (from a 750-ml bottle)
• 2 cups water
• 1/4 cup red-wine vinegar
• 1/4 cup balsamic vinegar
• 1 firm sweet apple, such as Honey Crisp, Gala, or Fuji, peeled and coarsely grated
• 1 1/2 tablespoons sugar
• 1 1/4 teaspoons salt
• 10 whole black peppercorns
• 2 whole cloves
• 1 Turkish or 1/2 California bay leaf
• Special equipment: a 6-inch square of cheesecloth; kitchen string

Instructions

1. Heat butter in a 6- to 8-quart wide heavy pot over moderately high heat until foam subsides, then cook onion and cabbage, stirring frequently, until wilted and slightly browned, about 20 minutes.
2. Add wine, water, vinegars, apple, sugar, and salt and bring to a boil.
3. Wrap peppercorns, cloves, and bay leaf in cheesecloth and tie with string. Add to cabbage mixture, then cover cabbage directly with a round of parchment or wax paper and cover pot with lid. Reduce heat and simmer until cabbage is very tender, about 2 hours.
4. Discard cheesecloth bundle and season cabbage with salt and pepper.