Soak the Chinese noodles in hot water for about 15 minutes. Drain off the water.
In a deep saucepan, kettle, or wok, heat the oil and use it to fry the ginger and the leeks until they begin to brown.
Add all of the other vegetables and continue stirring for 5 minutes.
Add the noodles, the soy sauce, star anise, sugar, and the mushrooms and reserved liquid. Simmer for about 15 minutes, until all vegetables are cooked to your taste.
Mix the cornstarch with the cinnamon, and then add this to about ¼ cup water, stirring to mix well.
Dribble this mixture slowly into the vegetables, stirring constantly. When the mixture has thickened to your taste, add the tofu, stir gently to avoid breaking it, sprinkle with sesame seeds and serve.