Preheat a grill to medium; oil the grate. In a small bowl, combine the cumin, coriander and 1 tsp. salt. Rub the chicken with 3 tsp. of the spice mixture. Grill, turning once, until just cooked through, about 8 minutes. Transfer to a cutting board.
Meanwhile, in a large bowl, whisk together the lemon juice, honey and the remaining spice mixture. Whisk in the EVOO. Add the cherries, arugula and parsley; toss well to coat.
Thinly slice the chicken against the grain. Divide the salad among 4 plates and top with the chicken.