In a small saucepan, combine soy sauce, mirin, brown sugar, smashed garlic, and sliced ginger. Heat under medium-low until sugar dissolves, about 2-3 minutes. Remove from heat and let cool.

Fill a large pot with enough water to cover the eggs and add white vinegar. Bring to gentle boil. Carefully lower in room-temperature eggs using a slotted spoon. Cook for 7 minutes for jammy yolks.

Prepare an ice bath in a large bowl with ice and water. Transfer boiled eggs to ice bath for 8-10 minutes to cool rapidly.

Gently tap each egg on a hard surface to crack the shell, then roll to break shell further. Peel starting from the wider end.

Place peeled eggs in a glass container and pour cooled marinade over them. Ensure fully submerged, weigh down if needed. Seal and refrigerate for a minimum of 3 hours, preferably overnight.