Cut the leek lengthwise, remove the core, and slice thinly. Soak in water and drain. Crush the garlic clove with the flat side of a knife.

Place the chicken wings and all seasoning ingredients in a pot. Heat until boiling, skim off any foam, cover, and simmer on low heat for 15 minutes.

Remove the lid and simmer over medium heat until the sauce reduces by half. Turn off the heat, add boiled eggs, and coat them with the sauce. Let sit for 5 minutes.