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In a large pot, bring chicken broth to a simmer. Add carrots, celery, onion, garlic, and thyme. Cook for 10 minutes until vegetables begin to soften.
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Add the shredded chicken and season with salt and pepper.
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Make the dumplings: In a bowl, whisk together flour, baking powder, and salt. Stir in milk and melted butter until just combined. The dough should be sticky and imperfect — do not overmix.
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Drop the dumpling dough by heaping tablespoons into the simmering soup. Dip the spoon in hot broth between scoops so the dough slides off easily.
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Cover the pot with a tight lid and do not lift it for 15 minutes. The steam is what makes the dumplings fluffy.
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Remove the lid. The dumplings should be puffed up and cooked through. Serve immediately.