In a mixing bowl, whisk together the peanut butter, soy sauce, honey, lime juice, sesame oil, garlic powder, and ground ginger. Add water gradually to achieve a smooth and pourable consistency.
Shred or slice your cooked chicken breast into bite-sized pieces. Combine it with about three to four tablespoons of the prepared peanut sauce in a large bowl and toss well.
Rinse and shred your carrots and cabbage. Thinly slice your red bell pepper and chop the green onions.
Warm your tortillas slightly in the microwave or in a dry skillet over low heat until soft.
Lay one tortilla flat, place a portion of peanut-coated chicken in the center, and top with carrots, cabbage, bell pepper, and green onions. Drizzle more peanut sauce if desired.
Fold in both sides of each tortilla and roll tightly from the bottom up. Slice each wrap in half if desired.