Heat a large saucepan or Dutch oven, over medium heat.
Add oil, then onion and cook about five minutes until translucent.
Stir in carrot, garlic, and then bell pepper. Cook until tender.
Add broth, water, and cabbage. Bring to a boil, then simmer uncovered for about 20 minutes.
When cabbage has been reduced a bit so there is more broth visible, add the balsamic vinegar and hot sauce.
Season to taste with salt and pepper.