Combine the cabbage, carrots, onions and dry spice mix in a large bowl, and then pour in the vinegar and lime juice. Quarter the peppers or cut them into large chunks so that they add flavor but can be picked out if you don't want to eat them. Add the salt, and then mix the slaw thoroughly using your hands. Transfer to a quart jar, pour the remaining juice from the bowl on top and seal tightly.
Let the jar sit at room temperature for 24 to 48 hours. This will allow for a brief and mild fermentation - the longer it sits, the more sour the pickle will be.
Refrigerate the jar for another 12 to 24 hours to stop the fermentation process. Serve as a cold side with any entree, and store in the refrigerator.
This recipe was provided by a chef, restaurant or culinary professional and may have been scaled down from a bulk recipe. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results