Start by filling a pot with water and adding a generous pinch of salt. Bring to a boil. Carefully lower in the eggs and cover the pot. When boiling resumes, reduce heat and simmer for 11 minutes. Transfer eggs to an ice bath.

In a saucepan, combine soy sauce, dark soy sauce, brown sugar, and mirin. Stir over medium heat until gently simmering. Remove from heat and let cool while adding star anise and cardamom pods.

Once cooled, carefully peel eggs and place in a shallow dish. Pour the marinade over the eggs, ensuring they are submerged. Cover and refrigerate for 8 to 24 hours.

Slice each egg in half and scoop cooked yolks into a bowl. Mix yolks with white miso, mayonnaise, honey, and white pepper until smooth.

Fill the egg white halves with the yolk mixture. Garnish with shichimi togarashi and green onions. Optionally top with ikura and sesame seeds.