If you're expecting leftovers, serve the salad dressing on the side.
Combine cabbage, snow peas, carrots and radishes in a large serving bowl. Refrigerate until ready to serve.
Stir together mirin, ponzu, green onion and dry mustard in a small bowl. Whisk in oil slowly; refrigerate until ready to serve.
Rub both sides chicken breasts with seasoning.
Preheat grill to medium-high heat. Brush the cooking grates clean. Coat cooking grates with grill spray to prevent sticking.
Grill the chicken, over Direct Medium-high heat, with the lid closed, 12 to 16 minutes turning once. Remove from grill to cutting board; let rest 3 minutes before thinly slicing.
Place sliced chicken on top of salad. Pour dressing over top and toss to combine. Sprinkle with toasted almonds.
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