To prepare the dressing, combine the first 4 ingredients in a bowl, and stir well with a whisk. Set dressing aside.
Prepare grill or broiler.
To prepare salad, combine 1 tablespoon dressing and chicken, and toss to coat. Place chicken on a grill rack or broiler pan coated with cooking spray; cook 6 minutes on each side or until chicken is done. Cut chicken diagonally across grain into thin slices. Combine chicken, mango, shallots, and ginger. Toss with remaining dressing. Divide salad greens evenly among 3 plates. Top salad greens with chicken salad; sprinkle with mint.