In a large pot, melt butter over medium heat. Add onion, celery, and carrots; sauté for 5 minutes.
Add garlic, thyme, salt, and pepper; cook for 1 minute.
Place the whole chicken in the pot and cover with broth. Add the bay leaf.
Bring to a boil, then reduce heat and simmer for 25–30 minutes until the chicken is cooked.
Remove the chicken, shred the meat, and return it to the pot. Discard bones and bay leaf.
In a bowl, mix flour, baking powder, and salt.
Stir in milk and melted butter until a soft dough forms.
On a floured surface, roll the dough to ¼-inch thickness and cut into 1-inch squares.
Bring the stew to a gentle simmer. Drop dumplings into the broth one at a time.
Cover and cook for 10–12 minutes (do not stir; let dumplings steam).
Serve hot, garnished with fresh parsley if desired.
