Add the chicken stock, 1/2 cup kimchi, white miso, and soy sauce to a 3-quart pot. Mix well, then bring to a boil.
Add the ramen noodles and boil for 5 minutes, or until soft
Divide the noodles between two bowls. Top with eggs, scallions, and additional kimchi. Ladle the broth over the noodles and serve immediately.
To soft boil eggs, bring a saucepan of water to a boil. Fill a bowl with ice water. And two cold eggs to the boiling water and cook for 7 minutes. Use a slotted spoon to transfer the eggs to the ice water; let them sit for 2 minutes or until cool to the touch.