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1
In a large pot, heat the olive oil over medium-high heat until shimmering. Add the carrots and cook, stirring, until lightly softened, about 2 minutes. Add onion and celery. Cook, stirring, until vegetables are soft but not brown, about 7 minutes. Season lightly with salt and pepper. Add white rice flour and cook, stirring until flour just begins to brown, about 3 minutes. Whisk in the water in a slow, steady stream.
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2
Add the chicken thighs and chicken stock. Bring to a boil. Once it reaches a boil, skim surface of any scum, then lower heat to a bare simmer. Cook, uncovered, skimming a few times, until chicken is completely tender, about 1 1/2 hours (add extra water or chicken stock as necessary to keep chicken and vegetables submerged).
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3
Remove the chicken from the soup with a slotted spoon and place on a clean cutting board. Allow to rest until cool enough to handle, then shred meat with fingers or two forks, discarding the bones and any excess fat or gristle. Shred or chop chicken into bite-sized pieces and return to soup. Season soup to taste with salt and pepper. Keep warm.
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4
In a medium bowl, whisk together the white rice flour, cornstarch, sweet rice flour, parsley, baking powder, 1 teaspoon salt, and xanthan gum. Add the milk and eggs and stir to combine.
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5
Bring soup to a bare simmer. Scoop the dough, about 2 tablespoons at a time, onto the top of the soup. You will get about 15 dumplings. The dumpling batter will cover the top of the soup and touch. This is normal.
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6
As soon as you've added the last dumpling, cover the pot. Set heat to low, and cook for 20 minutes without opening cover. A tester inserted into the center of a dumpling should come out clean. Spoon into individual bowls or plates and serve hot. Store leftovers in the refrigerator for up to four days.
