Place a bowl of ice water next to the stove.
Place the eggs in a saucepan and cover completely with cold water. Bring to a boil, using a spoon to occasionally turn the eggs, and cook for 10 minutes.
Immediately transfer the eggs to the ice water. Once cool enough to handle, use a spoon to gently crack the eggs all over without removing the shell.
Empty the saucepan and add the soy sauce, water, brown sugar, and ginger. Bring to a boil, then add the cracked eggs. Reduce to a simmer, cover, and cook for 30 minutes. Remove from heat and allow to rest for another 30 minutes.
Peel the eggs and refrigerate until ready to serve.