Heat the olive oil in a large Dutch oven over medium heat. Add the celery, carrot, and onion. Cook until the vegetables soften.
Add the chicken leg quarters, 6 cups of water, thyme, sage, salt, pepper, and rosemary . Stir to combine.
Reduce the heat to low and cook for about 1½ hours, or until the chicken is tender and cooked through.
Carefully remove the chicken from the pot. Allow it to cool enough to handle, then remove the meat from the bones. Return the chicken to the pot.
Pour the chicken broth into the pot and bring the mixture to a simmer. Taste and add additional salt and pepper as needed.
In a small bowl, whisk together the cornstarch and cold water until smooth. Slowly pour the slurry into the simmering broth while stirring. Continue stirring until the broth begins to thicken.
In a medium bowl, combine the gluten-free flour, thyme, black pepper, salt, and baking powder.
Add the cold, cubed butter. Use a pastry cutter or fork to cut the butter into the flour mixture until it resembles coarse crumbs.
Use a spatula to stir in the milk until the dough comes together.
Use a spoon or 2-teaspoon cookie scoop to portion the dough into 12 dumplings.
Bring the broth to a gentle simmer. Carefully add the dumplings to the pot, spacing them evenly across the surface. Cover the pot and cook for 5–8 minutes, until done.
Serve.