For the cabbage: Heat 1 tbsp of oil in a heavy based saucepan over medium heat and cook onion, stirring often for 3 – 5 minutes, or until softened. Add the garlic and cabbage and cook for 3 minutes. Stir in vinegar and sugar and bring to a simmer. Cover, reduce heat to low and simmer for 20 minutes. Add carrot, cover and cook a further 15 – 20 minutes, or until cooked.