Step 1Mince the carrot, water chestnuts and mushrooms very fine; they must be small for the stuffing. Chop the soaked shrimp, if using, very fine.
Step 2Combine the carrot, water chestnuts, mushrooms, shrimp and pork. Add 1 teaspoon of sugar, 1/2 teaspoon of salt, a dash of white pepper, 1 teaspoon of sesame oil and 1 teaspoon of cornstarch. Mix well.
Step 3Cut off each end of the zucchini. Peel, using a potato peeler. Hollow out the center carefully, using a sharp thin knife or melon baller. Rinse the center cavities. Stuff as much of the pork mixture into the zucchini as possible. Form any remaining filling into marble-sized meatballs. Place the stuffed zucchini and the meatballs on a heatproof platter and set them on a rack in a steamer over simmering water. You can also set the rack over a roaster or pot large enough to hold the rack. Cover and steam until the squash is tender and the pork is cooked, 20 to 30 minutes.
Step 4Meanwhile, cut the bok choy leaves crosswise into 2-inch pieces, then slice vertically, but not too fine. Heat 1 tablespoon of vegetable oil in a wok over high heat. Add a little of the ginger and green onions and all the bok choy, 2 tablespoons of water, the wine, 1/3 teaspoon of sugar and a dash of salt. Cover and cook 1 minute, then add 1 teaspoon of sesame oil and 1 teaspoon of vegetable oil. Arrange this mixture on a large serving platter, leaving a clear space in the center for the zucchini.
Step 5Place the zucchini on the platter, reserving any liquid accumulated during steaming, and cut the zucchini crosswise into 1-inch slices. Set the meatballs aside.
Step 6Add the cooking liquid to the empty wok. Add 1/2 cup water, the remaining ginger and green onions, the soy sauce, 1 teaspoon sesame oil, 1 teaspoon salt, 1/2 teaspoon sugar and a dash of pepper. Add the meatballs. Mix 1 teaspoon of cornstarch with 2 teaspoons of water, add to the wok and mix gently. Cook over medium-high heat until thickened, about 2 minutes. Pour the meatballs and their sauce over the zucchini.