Place dried shiitake mushrooms in a medium-sized bowl and add water to cover. Rehydrate mushrooms until soft, 20 to 30 minutes (or according to instructions). Set aside.

Wash chicken carefully with tap water. Transfer to a large pot and add water to cover chicken. Cover pot and bring to a boil. Continue to cook over medium heat, uncovered, for 10 minutes. Use a large ladle to skim the foam from the surface. Try to leave the oil on top, however, because it will add a nice flavor to the dish later.

Transfer the chicken to a wok (or dutch oven). Pour in chicken broth until it almost completely covers the chicken. Add Shaoxing wine, ginger, and star anise. After bringing to a boil, simmer covered over low heat for 20 minutes.

While braising the chicken, prepare the mushrooms and other ingredients. Wash the shiitake mushrooms carefully with running water.

Add green onion, light soy sauce, dark soy sauce, sugar, and 1/2 teaspoon salt into the wok. Use a spatula to scoop the chicken from the bottom and mix the ingredients. Add rehydrated shiitake mushrooms and place tea tree mushrooms (or whichever type you’ve chosen) on top. Cover and bring to a boil over medium heat. Turn back to low heat and simmer covered until chicken turns soft, 20 to 30 minutes. Check the chicken every 10 minutes, scooping from the bottom with a spatula to avoid burning.

Taste a small piece of chicken and some sauce, adding salt if necessary. If you want to serve the chicken by itself, the chicken should taste slightly plain now, because the saltiness will increase once the sauce is reduced. If you want to serve the chicken over steamed rice, add a bit of salt until it tastes just right. In this case, I added 1/4 teaspoon of salt to get a slightly salty dish in the end.

Turn to high heat and boil uncovered. Use a spatula to scoop the chicken from the bottom constantly, until the sauce is thick enough to coat the chicken, 5 to 10 minutes.

Transfer chicken to a plate and serve warm over rice.

Store the leftover chicken in an airtight container in the fridge for up to 1 week or in the freezer for up to 2 months.