Fry tortilla strips in oil until lightly browned and crispy. Remove from oil. Drain and cool on paper towels.
Grill jicama slices for about 3 minutes (enough to mark with the grill and slightly soften). After grilling, cool jicama and slice in julienne strips.
Toss the jicama, peppers, cabbages and crispy tortilla strips together in a mixing bowl.
For the lime dressing whisk together the garlic, shallot, cilantro, oil, lime juice and salt. Pour the dressing over the salad and distribute evenly. Sprinkle the grated cotija cheese over the salad and mix well.
Blue Mesa Grill Dallas, Texas