Over medium-high heat, bring the chicken stock and miso paste to a boil. Cook for 3-4 minutes, or until the miso paste is well combined.
Add the chopped chicken. (You can use rotisserie chicken, or baked chicken for this).
Stir in the cornstarch slurry and cook for another 2-3 minutes, or until the broth has thickened slightly.
Slowly add in the beaten eggs. Allow them to cook for 2-3 minutes before stirring.
Taste the broth. Add more soy sauce, if desired. (Some store-bought chicken broth are saltier than others. Add more water if the broth is too salty. More soy sauce if not salty enough.)
To serve, ladle the soup into bowls. Top with green onion slices and freshly ground black pepper, to taste.