In a Dutch oven or kettle, heat oil and 1/4 cup brown sugar over medium heat. Add garlic; saute for 2 minutes. Stir in 2 cups cranberries and vinegar. Cover and cook over medium heat for 3-4 minutes or until the berries have popped.
Add cabbage and wine or apple juice. Cover and cook over medium heat for 15 minutes or until the cabbage is tender, stirring occasionally. Stir in the salt, cayenne and remaining cranberries and brown sugar. Remove from the heat. Cover and let stand for 5 minutes or until berries are tender.