Bring a medium pot of water to a boil and prepare an ice bath. Gently add eggs (cold from the refrigerator) into the boiling water and cook for exactly 6 ½ minutes. Remove and immediately place in the ice bath. Let cool. Peel the eggs.

Combine the tamari, mirin, ¾ cup water, and vinegar in a small bowl and whisk. Add the eggs. Place a paper towel soaked in marinade on top to keep eggs submerged. Cover with plastic wrap and refrigerate for 6–12 hours. Discard marinade. Serve eggs immediately or store in the refrigerator in an airtight container.