Whisk together the chicken stock, cornstarch, ground ginger, sesame oil, garlic powder, and pepper in a large pot until there are no clumps.
Place over high heat and bring to a boil, whisking occasionally.
While the broth cooks, beat the eggs in a spouted measuring cup (or bowl). Set aside
Once the broth is boiling, reduce the heat to medium and stir in a circular motion with a wooden spoon to create a whirlpool effect.
Continue to stir while slowly pouring in the beaten eggs until all the eggs are added. (This will create egg strings in the soup.) Check the seasoning of the soup and adjust to taste with salt and pepper.
Portion into bowls and garnish with sliced green onion before serving warm.
Notes
You can stir in the toasted sesame oil at the end after pouring the eggs if you prefer. I find that adding the oil later gives the soup a stronger lemon grass flavor. The soup can be prepared both ways, depending on your flavor preference.