Place 12 eggs in a saucepan and cover with cold water. Bring to a boil over high heat and boil hard for 15 minutes.
Remove the saucepan from heat and let the eggs cool in the cooking water until completely cool.
Gently tap and crack the shells all over with a spoon, creating fine cracks without removing the shell completely.
Coarsely crush the 2 pieces of star anise in a mortar and pestle.
Transfer the cracked eggs to a clean saucepan. Add the crushed star anise, 2 tablespoons salt, 4 tablespoons Chinese soy sauce, 4 teaspoons black tea leaves, and enough cold water to completely cover the eggs.
Bring to a boil over high heat. Reduce heat to low and simmer gently for 2 hours, adding water as needed to keep the eggs completely covered.
Remove from heat and let the eggs stand in the seasoning liquid at room temperature for 12 hours.
Peel the eggs and serve cold. The eggs require no additional seasoning as they are fully flavored from the cooking liquid. Serve as-is, sliced on bread, or eaten whole.