Prepare your mise en place by mincing garlic, ginger, and green onions into separate small bowls. Pat the diced chicken thoroughly dry with paper towels to remove excess moisture—this step is CIA-level critical for achieving maximum crispiness when cooking.
In a small bowl, whisk together soy sauce, rice vinegar, sesame oil, hoisin sauce, lime juice, white pepper, and your cornstarch slurry. Set this sauce mixture aside and allow flavors to marry for 2-3 minutes while you prepare the cooking station.
Heat 2 tablespoons vegetable oil in a large skillet over medium-high heat for exactly 2 minutes until it shimmers but doesn't smoke. Add the dried chicken pieces and cook undisturbed for 3-4 minutes to develop a golden crust on the bottom layer.
Stir the chicken and continue cooking for another 2-3 minutes until the pieces achieve golden-brown color on all sides. Add minced garlic and ginger, stirring constantly for 30 seconds until fragrant—don't skip this step as it blooms the aromatic oils throughout the crispy chicken lettuce wraps.
Pour the reserved sauce mixture into the skillet and add diced water chestnuts and shredded carrots. Toss gently for 1-2 minutes until the cornstarch thickens into a light glaze coating every piece of chicken. Add green onions in the final 30 seconds of cooking.
Transfer the warm chicken filling to a serving bowl and arrange butter lettuce leaves on a large platter. Guests assemble their own wraps by spooning filling into lettuce cups, creating an interactive dining experience.