In a large bowl, combine the ground chicken and minced green onions. Add the kosher salt and pepper, and mix together well. Form into a large patty. Mix together the rice wine vinegar, wine, soy sauce, and hoisin sauce in a bowl or measuring cup and set aside.
Heat a wok over high heat, or an electric wok to 400 degrees. Add the oil and when smoking, carefully set the ground chicken patty in the wok. Brown on one side, then carefully break up and add the garlic, ginger, and red pepper flakes. Continue to stir until the chicken is thoroughly browned, about 5 minutes. Add the rice wine vinegar mixture and cook, stiring, until the liquid has just about evaporated, about 5 minutes. Remove from the heat. Taste and adjust the seasonings. Stir in the cilantro or if desired, mint.
Cut away the base of the lettuce and remove the outer leaves. Use the smaller inner leaves for cups. Place 2 or 3 cups on each plate, or line a platter, top with salad and serve.