Heat 2 tbsp vegetable oil in a 6 qt dutch oven over low medium heat. Put the onions in and sweat (no color) for about 10 minutes. Stir occasionally. Keep the heat low, and do not brown the onions. Add the garlic and jalapeno after 10 minutes, and sweat for about 5 minutes. Stir occasionally.
Add the broth, bring to a soft boil, then add the rice. Return to a soft boil, then reduce to a simmer. Add the lime zest, juice, and soy sauce. Cover and simmer for 20-30 minutes.
Salt and pepper to taste. Add the cabbage, cover, and cook until tender. About 10 minutes.