Prepare the broth: In a medium saucepan, bring the chicken or vegetable broth to a gentle boil over medium-high heat. Add ginger, garlic, and white pepper. Allow the flavors to meld for about 2-3 minutes.
Thicken the soup (optional): Stir in the cornstarch slurry (1 tablespoon cornstarch mixed with 2 tablespoons of water) to slightly thicken the soup. Let it cook for another 2-3 minutes until the broth is slightly thickened.
Prepare the egg: Crack the eggs into a bowl and beat until well-mixed. Once the broth is gently simmering, slowly drizzle the egg into the soup while stirring in one direction with a fork or whisk. This will create delicate egg ribbons in the soup.
Season and garnish: Taste the soup and add salt and soy sauce if needed. Remove from heat and stir in the sesame oil (optional). Serve hot, topped with chopped green onions.