Hot and Sour Soup
Combine the water and dried kelp in a large pot, and heat on a stovetop until simmering. Add the bonito flakes and remove from the flame. Let the broth rest for 20 minutes. Strain the broth and season with soy sauce, fish sauce, white vinegar, and mirin. Reheat the broth on the stovetop, and add the chicken and hominy. As the broth begins to boil, add the eggs and stir to disperse. Cook until the eggs firm.
To Assemble and Serve:
Distribute the soup into bowls. Garnish with cilantro and bean sprouts.