Bring 2 quarts water, chicken, carrots, onion, celery, garlic, bay leaf, stock, and 1/8 teaspoon salt to a boil in a medium pot; skim froth. Reduce heat to medium-low; gently simmer 20 minutes. Add thyme.
Meanwhile, whisk together cornmeal, flour, baking powder, 1/2 teaspoon salt, shallot, zest, parsley, and cheese in a medium bowl. Add butter, and blend in with fingertips until the mixture resembles coarse meal. Add milk, and stir with a fork just until a dough forms.
Roll dough into 1-inch balls; add all at once to simmering broth. Cover; simmer, undisturbed, until the dumplings are cooked through, about 20 minutes. Divide soup among six bowls.