Prepare the broth: In a medium saucepan, bring the chicken or vegetable broth to a gentle boil over medium heat.
Make the slurry: In a small bowl, mix cornstarch with 2 tbsp water until smooth. Slowly whisk the slurry into the boiling broth to thicken slightly.
Season the soup: Add salt, white pepper, and soy sauce (if using). Reduce heat to low.
Add the eggs: In a separate bowl, lightly beat the eggs. Slowly drizzle the eggs into the simmering soup while stirring gently in one direction with a fork or chopsticks. The eggs will cook instantly into silky ribbons.
Finish & serve: Turn off the heat. Stir in sesame oil (if using) and garnish with chopped green onions. Serve immediately.