8 1/3-inch-thick rounds red onion
8 large shiitake mushrooms, stemmed
8 red radishes, trimmed, halved
4 baby bok choy, halved lengthwise
1 large orange bell pepper, cut lengthwise into 8 strips
1 1/4 cups Mango-Sesame Dressing, divided
6 boneless chicken breast halves with skin
Nonstick vegetable oil spray
Arrange all vegetables on large rimmed baking sheet. Brush vegetables lightly on both sides with 1/3 cup Mango-Sesame Dressing; sprinkle with salt and pepper.
Arrange chicken on sheet of foil. Brush both sides of chicken with 1/3 cup dressing, then sprinkle with salt and pepper. DO AHEAD Vegetables and chicken can be prepared 2 hours ahead. Let stand at room temperature.
Coat grill rack generously with nonstick spray and prepare barbecue (medium-high heat). Grill vegetables until just tender, turning occasionally, about 8 minutes for onion rounds and 4 minutes for mushrooms, radishes, bok choy, and pepper strips.
Return all vegetables to same baking sheet. Grill chicken until cooked through, 5 to 6 minutes per side. Transfer chicken to cutting board. Let stand 5 to 10 minutes. Cool 2 chicken breasts; wrap and chill for Asian Chicken-Noodle Salad.
Arrange remaining 4 chicken breasts and vegetables on platter. Serve with remaining dressing