Place chicken, water or broth, onion, garlic, bay leaves, thyme, and vinegar in a large pot and bring to a simmer.
Cook until chicken is tender, then remove chicken to cool; strain the broth if desired.
Shred the chicken meat, discarding bones and skin, and return meat to the pot.
Add carrots and celery to the broth and simmer until tender.
In a bowl, mix flour, baking powder, and salt for the dumplings.
Cut in the cold butter until the mixture resembles coarse crumbs.
Stir in the milk until a dough forms; turn onto a floured surface and roll thin.
Cut the dough into strips or squares.
Whisk cornstarch with a little cold water and stir into the simmering broth to thicken slightly.
Drop dumpling pieces into the pot one by one and cook for 10-15 minutes until tender and cooked through.