Make the sauce: Add peanut butter, honey (see note 2), olive oil, water, rice vinegar, soy sauce, pepper, and cayenne (if using) to a small, powerful blender. Blend until smooth. Refrigerate while preparing the rest of the recipe.
Chicken: Slice the chicken breasts in half horizontally and lightly pound to an even thickness. Season both sides with cumin, turmeric, salt, and pepper.
Heat butter and olive oil in a very large nonstick skillet over medium-high heat. Once the butter is melted, add the chicken in an even layer. Cook for 3 minutes, flip, then cook another 2 to 4 minutes, or until cooked through. Transfer to a plate and let rest for 5 to 10 minutes, then thinly slice against the grain or dice into small pieces.
Veggies: While the chicken cooks, slice the pepper, carrots, and cucumber into matchsticks and finely chop the peanuts.
Assemble: Wash and thoroughly dry the lettuce leaves. Divide the chicken evenly among the 12 leaves, then top with bell pepper, carrots, cucumber, and peanuts. Finish with fresh cilantro, drizzle generously with peanut sauce, and serve right away with lime wedges on the side.
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Notes
Note 1: To use ground chicken, cook it in a large skillet with the butter and olive oil, breaking it up as it cooks. Season the same way and cook until fully cooked and lightly browned. Adjust seasonings to taste, then assemble the wraps as directed.Note 2: English or mini Persian cucumbers work best since they are crunchier and have fewer seeds. When cutting into matchsticks, discard the seedy center.Note 3: This sauce is intentionally sweet. For less sweetness, add the honey gradually to taste, or balance it with extra cayenne or red pepper flakes.Storage: Store cooked chicken, prepped veggies, and peanut sauce in separate airtight containers in the fridge. The chicken and veggies keep well for up to 4 days, and the sauce lasts up to 2 weeks. Assemble wraps just before eating for the best texture and flavor.