In a small bowl, whisk together the peanut butter, soy sauce, lime juice, honey, minced garlic, and a splash of water to desired consistency. If you like a little heat, add crushed red pepper or chili flakes. This will be your sauce base.
If your chicken isn’t already shredded, shred or chop it into bite-sized pieces. Place the chicken in a large mixing bowl and toss with half of the peanut sauce until well coated.
In a separate bowl, combine the cabbage, carrot, cucumber, red pepper (if using), cilantro, and green onions. If you want a touch of acidity, drizzle a teaspoon of rice vinegar and a tiny bit of sesame oil over the veggies and toss lightly.
Warm the tortillas gently (in a dry skillet over medium heat for about 15–20 seconds per side, or wrap in a damp towel and microwave for 15 seconds) to make them more pliable.
To assemble, lay a tortilla flat. Start with a bed of greens or lettuce if using, then add a spoonful of the dressed chicken in the center. Top with a generous portion of the veggie mix, and finish with another drizzle of the peanut sauce and a sprinkle of cilantro and green onions.
Fold in the sides and roll tightly to enclose the filling. If desired, brush the outside with a little oil and warm in a skillet for 1–2 minutes per side to lightly toast the tortilla and meld flavors.
Serve immediately with lime wedges on the side for extra brightness. These wraps are delicious warm or at room temperature, making them great for meal prep.