Run the celery and onion through a food processor and chop them finely.
In a large Dutch oven, add the butter, olive oil, celery, onion, salt, pepper, and thyme. Cook over medium heat for about 5–10 minutes, or until the vegetables begin to soften.
Add the chicken and chicken broth. Bring the mixture to a boil, then reduce the heat and simmer for about 15 minutes, or until the chicken is cooked through.
While the chicken is cooking, prepare the dumplings.
In a large bowl, whisk together the gluten-free flour, salt, and baking powder. Stir in the milk until a dough forms.
Turn the dough out onto a generously floured surface. Roll the dough to about ¼-inch thickness. Using a pizza cutter, cut the dough into strips approximately 1–2 inches long.
Once the chicken is cooked through, remove it from the broth and cut it into bite-sized pieces. Return the chicken to the Dutch oven.
Add the dumplings to the simmering broth. Cook for about 20 minutes, stirring occasionally, until the dumplings are cooked through and the broth has thickened.
Taste and season with additional salt and pepper as needed.
Serve hot and enjoy.