Season the chicken breasts with salt and pepper to taste.
Grill chicken over medium-high heat for 6-7 minutes per side or until the internal temperature reaches 165°F (74°C).
Transfer chicken to a cutting board and let rest for 5 minutes before slicing into 1/2-inch strips.
In a small mixing bowl, whisk together soy sauce, rice vinegar, sesame oil, grated ginger, minced garlic, and honey until emulsified.
In a large salad bowl, combine mixed greens, shredded cabbage, julienned carrots, and sliced cucumber.
Drizzle half of the dressing over the vegetables and toss gently to coat.
Arrange the sliced chicken on top of the greens.
Garnish with toasted sesame seeds and sliced almonds, then drizzle with the remaining dressing.