Finely dice the shiitake mushrooms, carrots, and water chestnuts into uniform pieces.
In a small glass bowl, whisk together the tamari, rice vinegar, and honey until the honey is fully dissolved.
Heat the toasted sesame oil in a large stainless steel skillet or wok over medium-high heat.
Add the ground chicken to the skillet, seasoning with sea salt and black pepper, and cook while breaking it apart until fully browned.
Stir in the minced garlic and fresh ginger, sautéing for approximately 60 seconds until the aromatics are fragrant.
Add the diced mushrooms, carrots, and water chestnuts to the pan and cook for 3-4 minutes until the vegetables are tender yet retain a slight bite.
Pour the prepared sauce over the chicken and vegetable mixture, tossing for 1 minute until everything is evenly coated and the sauce has thickened slightly.
Carefully spoon the warm chicken mixture into the iceberg lettuce leaves.
Garnish each cup with thinly sliced green onions and crushed cashews for added texture before serving.