While the mushrooms soak, whisk together 4 teaspoons of cornstarch, wine, and light soy sauce in a medium bowl. Add the chicken and mix well.
In a small bowl, whisk together 2 tablespoons cornstarch, sugar, hoisin sauce, dark soy sauce, chicken broth, and chili-garlic sauce. Make sure the cornstarch is completely dissolved.
Drain the mushrooms and squeeze them dry. Remove the stems and discard, then chop the rest into bite-size pieces. In a medium bowl, combine the mushrooms, bamboo shoots, water chestnuts, celery, thawed peas, and scallions.
Pour the canola oil into the bottom of a cold wok and add the sliced ginger. Heat until the wok and oil are very hot and the ginger releases its fragrance. Remove the ginger and discard. Add the chicken mixture and cook while stirring until the chicken is cooked and crumbly, about 3 to 4 minutes. Add the vegetables and stir well, cooking until they are heated through, about 2 to 3 more minutes. Stir in the sauce and continue cooking for about 1 more minute. Drizzle the sesame oil over it all and stir. Transfer to a serving bowl or platter and serve with the lettuce leaves and rice.