Melt 2 tablespoons butter in a large Dutch oven over medium heat. Add onion, carrots, and celery and cook for 5 to 6 minutes until softened. Add garlic and cook 1 minute more.
Pour in chicken broth and bring to a boil. Add shredded chicken, dried thyme, salt, and pepper. Reduce heat to a gentle simmer.
While the stew simmers, make the dumplings. Whisk together gluten free flour, baking powder, and salt. Stir in milk, melted butter, and parsley until a thick, sticky dough forms.
Drop rounded tablespoons of dumpling dough onto the surface of the simmering stew, spacing them slightly apart. You should get about 12 dumplings.
Cover the pot with a tight-fitting lid and simmer for 15 to 18 minutes without lifting the lid. Dumplings are done when they are fluffy and cooked through. Serve immediately in bowls.