4 tablespoons (2 ounces) unsalted butter, cut into tablespoons
1 tablespoon sugar
1 teaspoon coarse salt
1/3 cup water
1/3 cup distilled white vinegar
1 small head red cabbage (2 pounds), cored and thinly shredded
1/4 cup red-currant jelly
3 tablespoons peeled, coarsely grated Granny Smith apple (about 1/2 apple)
Preheat oven to 325 degrees. Combine butter, sugar, salt, water, and vinegar in a Dutch oven or an oven-proof pot over medium heat. Bring mixture to a boil, stirring until butter melts and sugar dissolves.
Add cabbage, and toss to combine. Cover and place in oven. Bake, stirring once halfway through, until cabbage is wilted and tender, about 1 hour and 50 minutes.
Stir in jelly and apple, cover, and bake 10 minutes more. Let stand, covered, until ready to serve (or for up to 1 hour; rewarm gently over low heat).