Heat a soup pot or Dutch oven over medium-high heat, then coat with 1 tablespoon of oil.
Season chicken thighs with herbes de Provence and sea salt, brown on both sides briefly, then set aside.
Add remaining oil and sauté onion, carrots, celery, garlic, and sage for 4–5 minutes.
Deglaze with sherry, scraping the pan, then return chicken and add broth.
Bring to a boil, then simmer for 15–20 minutes.
For dumplings, mix flours, xanthan gum, baking powder, parmesan, and salt in a bowl.
Stir in egg and butter, then roll into 1-inch balls.
Shred cooked chicken and stir in heavy cream.
Add dumpling balls, cover, and simmer for 12–15 minutes until dumplings double in size.
Serve hot with extra parmesan, salt, and fresh herbs like sage or thyme.