SAUCE: To a small powerful blender jar (I use a mini Blendtec/twister jar) add 1/4 cup creamy peanut butter, 3 tablespoons honey (See Note 1), 2 tablespoons olive oil, 1 tablespoon + 2 teaspoons water, 1 and 1/2 tablespoons rice vinegar, 1 and 1/2 tablespoons low sodium soy sauce, 1/8 teaspoon pepper, 1/8 teaspoon cayenne pepper (optional, depending on your preference for heat), and 1/4 teaspoon salt. Blend until smooth and refrigerate while preparing everything else.
CHICKEN: Remove fat and halve breasts lengthwise if they are thick. Pound chicken to get the pieces uniformly thick throughout. (You can pound them with a meat mallet or the bottom of a heavy frying pan.) Pat both sides of the chicken with paper towels. On one side of the chicken, drizzle 1/2 tablespoon olive oil and rub it in. Sprinkle on half of the salt, half of the pepper, half of the turmeric, and half of the cumin. Gently press in the spices and then flip the chicken to the other side. Drizzle with the remaining olive oil and spices.
CHICKEN CONT.: Preheat an indoor or outdoor grill for medium-high heat (400-450 degrees F on an outdoor grill) and generously oil the grates (Note 2). Cook on the preheated grill until the chicken is golden and no longer pink in the center, about 4-5 minutes per side (or until the chicken registers 165 degrees F). Remove, cover with foil, and let stand for 5-10 minutes. When cooled slightly, dice the chicken into bite-sized pieces. To saute the chicken instead, see Note 3.
VEGGIES: Prep veggies while chicken is cooking: Slice a bell pepper into small matchstick-sized pieces, cut matchstick carrots (or use prepared matchstick carrots). Cut the cucumber(s) into matchstick pieces. If you aren't using salted nuts, add a pinch of salt to the veggies. Finely chop the peanuts.
ASSEMBLY: Wash and completely dry 12 lettuce leaves. Divide the cooked chicken evenly among the 12 lettuce leaves, followed by the veggies and peanuts. Add fresh cilantro and lime wedges to plates. Drizzle sauce generously over the wraps and enjoy immediately.