Heat a grill pan over high heat. Toss the chicken with soy sauce and oil and grill for 6 minutes on each side.
Combine the cucumber, sprouts, carrots, scallions, basil, mint and sesame with a generous sprinkle of sugar and vinegar. Season the salad with salt, to taste.
Whisk the peanut butter, soy sauce, vinegar and cayenne together. Stream in the vegetable oil.
Slice the cooked chicken on an angle. Toss with the veggies and herbs.
In a very hot nonstick skillet, or over a gas burner, heat the tortillas for 15 seconds on each side.
Pile the chicken and veggies in the wraps and drizzle liberally with spicy peanut sauce before wrapping and rolling.