Place eggs in a pot. Cover with about 1 inch water. Remove eggs and stir vinegar into the water. Bring to a boil. Gently place eggs back in. Cover and cook for 5 minutes to soft-boil. Cook 3 minutes more for hard-boiled eggs. Prepare an ice bath in the meantime.
Remove heat heat and immediately place eggs in the ice bath. Peel eggs carefully.
Combine soy sauce, ponzu sauce, mirin, scallions, garlic, brown sugar, sesame oil, togarashi, and ginger in a container such as a jar. Mix well to ensure the sugar dissolves and the garlic breaks up.
Place eggs in the mixture and seal. Marinate for 1 day. Eggs keep for 3 or 4 days after.