In a mixing bowl, combine the thinly sliced chicken breast with soy sauce and sesame oil. Marinate for about 15-20 minutes.
While the chicken is marinating, prepare the peanut sauce by whisking together peanut butter, honey, lime juice, and a pinch of salt until smooth. If the sauce is too thick, you can add a tablespoon of warm water to loosen it up.
Heat a non-stick skillet over medium-high heat and cook the marinated chicken for about 5-7 minutes, or until fully cooked and golden brown, stirring occasionally.
Once the chicken is cooked, remove it from the heat and set aside.
Lay out the large lettuce leaves on a clean surface or plate. In the center of each leaf, place a portion of the cooked chicken, followed by shredded carrots, red cabbage, cucumber, and cilantro.
Drizzle generous amounts of the peanut sauce over the fillings.
Carefully fold the sides of the lettuce leaves over the filling and roll them up tightly like a burrito.
Secure the wraps with toothpicks if necessary and garnish with chopped peanuts on top.
Serve immediately with extra peanut sauce and Sriracha sauce on the side, if desired.