Reconstitute the dried shiitake mushrooms in a bowl of hot water. Cut the garlic scapes into 2 inch sections, discarding the flower buds, and set aside. Julienne the carrots into about 1/8 inch thick pieces and set aside. Cut each baby corn in half on the bias and set aside. Cut the shiitake mushroom into 1/8 inch thick strips and set aside.
Mix the vegetarian stock or water with light soy sauce, sugar, cornstarch and ground white pepper in a small bowl. Set the sauce mixture aside.
Heat the vegetable oil in a wok until just about reaching smoking point. Add the garlic and ginger slices and stir-fry for about 30 seconds. Add the carrot slices and garlic scapes to the wok. Pour the cooking wine into the wok and stir-fry for about 30 second. Cover and let the vegetables steam in the wok for about one minute. Uncover and add the baby corn and mushrooms and continue to stir-fry for another 30 seconds. If the vegetables are dry when stir-frying, then add an additional 1/4 cup of vegetable stock or water. Pour the sauce mixture into the wok and let it thicken. Plate the vegetables and serve immediately.