In a large saucepan, gently add uncooked eggs and 1 teaspoon salt; cover with cold water. Bring to a boil, reduce heat, and simmer for 20 minutes. Remove from heat, drain, and cool completely. Tap eggs with the back of a spoon to crack shells only, DO NOT REMOVE SHELLS.
Combine 3 cups water, soy sauce, black soy sauce, salt, tea leaves, star anise, cinnamon stick, and tangerine zest. Bring to a boil, then reduce heat, cover, and simmer for 3 hours. Remove from heat, add eggs, and let steep for at least 8 hours.
Eggs can remain in soy/spice broth up to 1 1/2 days for richer flavor. Store eggs unpeeled and tightly sealed in refrigerator. They will keep 4 to 5 days.