Add the chicken stock and soy sauce to a large pot. Bring to a boil. Reduce the heat to a simmer. Add the chicken and mushrooms. Cook about 4 minutes. Add the tofu, pepper, and vinegar to the pot. Cook 2 minutes. Stir in the cornstarch mixture and cook until thickened whisk in the egg. Cook about two more minutes whisking constantly. Add the sesame oil. Ladle into bowls and garnish with scallions.