Bring soup stock, grated ginger and soy sauce to a boil. In a small cup, make a slurry by combining the cornstarch and 2 tablespoons of chicken stock. Stir until dissolved. Slowly pour in the cornstarch mixture while stirring the stock, until thickened. Reduce heat to a simmer. Pour in the eggs slowly while stirring the soup in the same direction. The egg will spread and feather. Turn off the heat and add the green onions and carrots. Season with salt and pepper, and serve immediately.