1. In a large bowl, whisk together 2 Tbsp. lime juice, mustard, salt and pepper. Whisk in oil and shallot.
2. Using a sharp knife, cut ends off jicama and peel by cutting from top to bottom. Cut jicama into matchstick-size pieces and toss with remaining 1 tsp. lime juice.
3. Just before serving, add jicama, radishes and mango to bowl with dressing. Toss well to coat. Line a serving platter with lettuce leaves, if desired, and pile salad in center. Sprinkle with parsley and serve.