In a small bowl, whisk together the soy sauce, sesame oil, rice vinegar, grated ginger, minced garlic, and honey.
Place the chicken breasts in a shallow dish and pour the marinade over the top. Let marinate for at least 15 minutes.
Preheat grill to medium-high heat. Remove chicken from marinade and grill for 6-8 minutes per side, or until cooked through.
Let the chicken rest for a few minutes, then slice into thin strips.
In a large bowl, toss together the mixed salad greens, red bell pepper, cucumber, and green onions.
Top the salad with the grilled chicken slices and sprinkle with toasted sesame seeds.
Serve with the sesame ginger dressing on the side.