Sauté onion in butter in a large deep skillet or Dutch oven until tender. Sprinkle with salt and pepper. Cook onion 15 more minutes or until caramelized, stirring often.
Toss shredded cabbage with vinegar and sugar. Gradually add to caramelized onion in skillet, stirring well. Cover and cook over medium heat 25 minutes or until cabbage is tender. Serve warm.