In a small bowl, combine the vinegar, garlic, mustard, 1/2 teaspoon of the salt, and 1/4 teaspoon of the pepper, whisking to dissolve the salt. Whisk in the olive oil. Set aside.
Prepare the grill to high heat and lightly oil the grate. Sprinkle the chicken with the remaining 1 teaspoon of salt and 1/2 teaspoon of pepper. Grill until cooked through, 3 to 4 minutes per side. Remove the chicken from the grill and let it rest for 5 minutes.
Meanwhile, in a large bowl, combine the greens, onion, and about half of the dressing. Arrange the mixture on plates or a platter.
Slice the chicken. Arrange the chicken, peas, and radishes on top of the greens. Drizzle with the remaining dressing, sprinkle with the cheese, and serve.Copyright Jill Silverman Hough. All rights reserved. www.jillhough.com.