1. Build a high-heat fire, with the flames licking the grill grate. Let it burn for 30 minutes.

2. Place the eggs in a Dutch oven or a medium pot with water to cover. Bring the pot to a boil over the fire, then adjust the heat to medium-low and simmer for 3 minutes. Remove the eggs with a slotted spoon (do not discard the water) and let them cool until one can handle them without scorching one's fingers. Tap the eggs with the back of a spoon to crack the shells evenly all over.

3. Return the eggs to the pot and add the remaining ingredients. Bring the water to a boil, reduce the heat, and simmer for 1½ hours. Add water to cover the eggs if they become exposed to the air. Remove the pot from the heat and let the eggs cool completely in the water.

4. Carefully peel away the shells, slice them in half lengthwise, and arrange them on a platter. Serve with more tea, preferably Chinese in origin.