Place the drumsticks in a deep pan and add the simmering liquid ingredients. Simmer over medium-low heat for about 30 minutes.
Place the eggs in a pot of cold water with a pinch of salt. Turn the heat to high and cook for 15 minutes total, hard-boiling the eggs. Place in the sink and run under cold water until cool enough to handle, then peel and set aside.
When the chicken has simmered for 30 minutes, add the boiled eggs to the pan, turn off the heat and cover. Leave the eggs to soak in the simmering liquid with the chicken for at least 30 minutes, turning occasionally to make sure they’re evenly coated. Cut the eggs in half before serving for some added colour.