Fill a medium saucepan with enough salted water to cover the eggs by an inch. Bring to a boil, then gently add the large eggs. Cover the pan and reduce heat to medium, cooking for exactly 11 minutes.

Transfer eggs into a bowl filled with ice water to cool them quickly for about 10 minutes.

Combine equal parts soy sauce, dark soy sauce, brown sugar, and mirin in a small saucepan. Heat until the sugar dissolves, about 3-5 minutes, and cool to room temperature.

Peel the cooled eggs and submerge them in the cooled marinade in a shallow dish. Refrigerate for at least 8 hours.

Remove the yolks and mix with miso, mayonnaise, honey, and white pepper until creamy and smooth.

Slice the eggs in half, scoop out the yolk filling, and fill each egg white with the mixture. Garnish with shichimi togarashi and diced green onions.