Place tofu on several paper towels. Cover with several more paper towels; top with a heavy skillet for 10 minutes to drain tofu. Throw paper towels away and cut tofu into 1/2 inch pieces.
Heat a tablespoon of olive oil in a large Dutch oven or stock pot over medium high heat. Add in the mushrooms and saute for five minutes. Add in the ginger, sugar, pepper, and garlic and saute for one minute.
Add in the chicken broth and 1 ½ cups of the water to the pot and bring to a boil. Reduce heat and simmer for 15 minutes, stirring occasionally.
In a small bowl combine cornstarch and remaining ½ c. water. Whisk until smooth. Slowly stir the cornstarch mixture into the soup. Add tofu and bamboo shoots and bring to a boil.
Cook for 5 minutes then remove from heat.
In a small bowl beat the egg. Slowly drizzle the egg into the soup (it will form ribbons of egg). Do not stir!
Return soup to low heat and cook 2-3 minutes. Sprinkle with green onions and drizzle with chili oil. Serve with crunchy noodles on top.