Combine the soy sauce and honey in a small bowl. Set aside.
Heat the oil in a large skillet over medium-high heat.
Season the chicken with ½ teaspoon pepper and cook, stirring occasionally, until it begins to brown, about 3 minutes.
Lower heat to medium and stir in the garlic and ginger. Add the scallions and cook for 1 minute.
Stir in the water chestnuts and half the soy sauce mixture. Continue cooking until the chicken is cooked through, about 4 minutes. Remove from heat and sprinkle with the cashews.
Divide the lettuce leaves among plates and spoon the chicken over the top. Serve with the remaining soy sauce mixture for drizzling