In a small bowl, combine 1/4 cup chicken broth and the cornstarch; mix well and set aside.
In a soup pot, combine the remaining chicken broth, the tofu, mushrooms, soy sauce, vinegar, ginger and pepper; mix well and bring to a boil over high heat. Reduce the heat to low; stir in the cornstarch mixture until thickened.
Slowy stir in the beaten egg to form egg strands.
Add the bean sprouts and simmer for 1 to 2 minutes, or until heated through, stirring occasionally. Add the sesame oil; mix well and serve.