Step 1Remove the tough cores of the cabbages and slice the leaves into thin strips about 1 inch long and one-fourth inch wide. Place the cabbage in a large bowl and add the carrots, pepper, green onions, olives and jalapenos. Toss until the ingredients are well dispersed.
Step 2Place the mayonnaise, brine, vinegar and oil in a small bowl and whisk to combine. Stir the dressing into the vegetables and toss until well mixed. Taste and add more mayonnaise or vinegar if desired. Season with salt and pepper to taste. Chill at least 1 hour before serving.