If using dried shitake mushroom, cover them in boiling water and allow to soak while you prep other ingredients.
Add 3 tablespoons sugar and 3 tablespoons oil to a cold wok, pan or clay pot and heat over medium-low heat until it caramelizes and turns light golden brown. Turn up the fire and add the chicken pieces, stirring and cooking in the caramel until they lose their pink color and all the watery fat cooks off.
Add the chicken broth, Shaoxing wine, salt and ginger and bring to a boil. Reduce heat, cover the pan and let cook at a simmer for about 10 minutes, stirring occasionally.
While the chicken is cooking, slice the shitake mushrooms thinly and cut the celery and scallions. Add the mushrooms, celery and scallion whites to the wok after the first 10 minutes of cooking. Return to boil, cover and continue to simmer on low heat another 10 to 15 minutes, stirring occasionally.
When the vegetables are done to your liking, add the scallion greens to the pot and then the cornstarch mixture. Stir until the broth thickens. Serve in a bowl, accompanied by rice.