Heat the oil over medium-high heat in a dutch oven or large pot. Add the onions, carrots and celery and cook for 5 minutes, stirring occasionally.
Stir in the garlic and cook for 30 seconds or until garlic becomes fragrant. Stir in the cabbage, jalapeno, ham, ½ tsp salt and ½ tsp pepper.
Stir in the chicken broth and bring to a boil. Reduce heat to low, cover and simmer stirring occasionally until cabbage is tender, about 20 minutes.
