In a small bowl, soak shitake mushrooms in warm water for about 30 minutes or until softened. Drain and squeeze out liquid. Stem mushrooms and mince. Set aside.
In a pan over medium heat, heat about 1 cup of oil until hot. Add noodles and deep-fry for about 10 to 15 seconds or until puffed up and color changes to white. Using a slotted spoon, remove from pan and drain on paper towels. Set aside.
In a bowl, combine chicken, one tablespoon of the soy sauce, Chinese cooking wine, and cornstarch. Marinate for about 10 to 15 minutes.
In a small bowl, combine hoisin sauce, the remaining one tablespoon soy sauce, and rice vinegar. Whisk together until blended and set aside.
In a wide skillet over medium heat, heat about 1 tablespoon oil. Add garlic and ginger and cook, stirring regularly, until aromatic.
Add chicken and cook, breaking apart with the back of a spoon, until lightly browned.
Add water chestnuts and mushrooms. Continue to cook for about 2 to 3 minutes or until vegetables are tender-crisp.
Add hoisin sauce mixture and stir until chicken is well coated. Continue to cook for about 3 to 5 minutes or until sauce is absorbed and chicken is cooked through.
Add green onions and stir to combine.
Remove from heat and transfer onto a serving platter. To serve, spoon chicken mixture into center of lettuce leaf and top with fried noodles.