Put 3 cups of broth in a pot and set to boil. Blend the eggs along with a tablespoon of soy sauce and the remaining cup of broth. When the broth is boiling, reduce the heat so it's just bubbling steadily and pour the egg mixture in, stirring constantly.
The mixture should resemble a thick, opaque liquid. Stir once every thirty seconds or so. The egg will cook in the broth. You'll know it's done when the mixture resembles clear soup with lots of floating scrambled egg bits. Add a teaspoon of sesame oil, a teaspoon of soy sauce, and pepper to taste. Drop in the scallions and serve.