Using a food processor fitted with the shredding disk, shred the jicama and apples. Transfer to a serving bowl and toss with 2 tbsp. lime juice.
In a small bowl, whisk together the remaining 2 tbsp. lime juice, the honey, 1/2 tsp. salt and 1/4 tsp. pepper. Whisk in the EVOO. Add the dressing and cilantro to the slaw; toss to coat.