Warm a stockpot over medium heat, add the oil, then cook the chopped onion until softened before stirring in the garlic for 1 minute. The onion should look translucent and smell sweet, and the garlic should be fragrant without browning.
Add the chicken and pour in the broth, bring it to a gentle boil, then lower the heat and simmer for 20 minutes until the chicken is cooked through. The meat should feel tender enough to shred or chop easily after you lift it out with a slotted spoon.
Cut or shred the chicken into bite-sized pieces and return it to the pot while the soup stays at a gentle simmer. The broth should stay calm and lightly steaming rather than reducing aggressively.
Whisk the almond flour, coconut flour, xanthan gum, baking powder, salt, and pepper in a medium bowl, then whisk the melted butter, coconut milk, and egg in a small bowl and stir the wet mixture into the dry just until a soft dough forms. The dough will feel sticky at first, then tighten quickly as the coconut flour absorbs moisture, so stop mixing once it holds together.
Shape the dough into 1-inch dumplings with your hands, pressing each one firmly several times so it stays compact. The dumplings should feel soft but packed, not crumbly or loose around the edges.
Stir the salt, pepper, and heavy cream into the soup, taste, and adjust the seasoning if needed, then reduce the heat to low. The broth should look creamy and smooth, with only a very light simmer at the surface.
Drop the dumplings into the soup one or two at a time and cook them for about 5 minutes, or turn off the heat just before adding them if your stove runs hot. Keep the pot uncovered only until the dumplings are added, then let the broth stay very gentle so they cook through without breaking apart.