Put 1/4 cup beef broth in a glass measuring cup or bowl. Set aside.
In a large Dutch oven, mix together the remaining beef broth, bamboo shoots, rice vinegar, soy sauce, ginger, and chili garlic sauce. Heat over medium-high heat until the soup reaches a simmer.
Add the cornstarch to the 1/4 cup of beef broth and whisk together until smooth.
After the soup begins to simmer, pour in the cornstarch mixture. Stir until the soup thickens.
Stir the soup in a circular motion, drizzle in a portion of the whisked egg in thin streams and continue stirring. Repeat this process until all of the eggs have been incorporated.
Add half of the green onions and sesame oil. Salt and pepper to taste.
Garnish with the remaining green onions.
Serve.