Season chicken breasts with salt and pepper, then grill or pan-sear over medium-high heat for 5-7 minutes per side until internal temperature reaches 165°F (74°C).
Allow chicken to rest for 5 minutes, then shred using two forks or slice into thin strips.
In a medium mixing bowl, whisk together peanut butter, soy sauce, honey, lime juice, ginger, garlic, and sesame oil.
Gradually whisk in warm water one tablespoon at a time until the sauce reaches a smooth, pourable consistency.
In a large bowl, combine the shredded chicken with 1/4 cup of the peanut sauce and toss to coat thoroughly.
Lay tortillas flat and distribute the red cabbage, carrots, and cucumber evenly across the center of each.
Top the vegetables with the peanut chicken mixture, green onions, and cilantro.
Drizzle the remaining sauce over the fillings.
Fold in the sides of the tortillas and roll tightly to secure.
Slice diagonally and serve.