Heat cooking oil in a medium dutch oven or other heavy pot over medium-high heat. Cook onions, stirring occasionally, until fragrant, about 30 seconds.
Add carrots and celery and season with some salt. Cook, stirring frequently, until the carrots and celery have softened a bit, and are starting to brown, about 5 minutes.
Using a spatula, push the carrots, onions and celery to the side of the pan. Place in the chicken thigh, skin down, so as much of the skin is touching the bottom of the pot. Cook for about 5 minutes, until the chicken skin has browned. The bottom of the pan should have brown bits stuck to it too. Flip the chicken, and continue cooking and mixing everything together, until the outside of the chicken thighs look cooked. The inside will still be raw.
Deglaze the pan by adding in a bit of water and scraping the bottom of the pan to remove and dissolve all the browned food bits from the pan. This will provide a rich flavor for the soup.
Add in the rice and stir everything together. Bring to a low boil, then turn the heat to low, cover, and simmer for about 20 minutes. When everything is just about cooked, add in the reconstituted wood ear mushrooms and simmer for another 5 minutes. The wood ear mushrooms only need to cook for a few minutes, and will not soften completely. Check and stir as needed during the cooking time. Remove from heat when done.
Using tongs, transfer the chicken thighs into a large bowl. Allow to slightly cool, then remove the skin and bones. Cut up the chicken into bite sized pieces, and return back to the soup.
Serve and enjoy!