Drain mushrooms and chop. Put chicken into a pan with oil and fry over moderate heat for 2 minutes. Add the oil and ginger and fry for 1 minute. Add the garlic and onions and stir-fry for another minute. Add the water, soy sauce, sugar, carrots, potatoes, mushrooms, and scallions. Cover the pan and cook over low for 25 minutes. Stir occasionally. Add sesame oil and cook for 5 minutes. Serve with rice.