Poach the chicken: In a large pot, add the chicken, broth, onion, celery, bay leaf, and a pinch of salt. Bring to a gentle simmer.
Cook until the chicken is just cooked through, about 15–20 minutes.
Shred the chicken: Remove the chicken to a plate and let it cool slightly. Discard the onion, celery, and bay leaf. Shred the chicken into bite-sized pieces with two forks.
Taste the broth: Skim any foam.
Adjust seasoning with salt and pepper. Keep the broth at a low simmer.
Make the dumpling dough: In a bowl, whisk 2 cups flour, 1 teaspoon salt, and 1 teaspoon baking powder (if using). Cut in the cold butter with your fingertips or a pastry cutter until the mixture looks like coarse crumbs.
Stir in the milk until a soft dough forms.
Rest the dough briefly: Let the dough sit for 5 minutes. This relaxes the gluten and makes rolling easier.
Roll and cut: Lightly flour your counter. Roll the dough to about 1/8–1/4 inch thick.
Slice into strips about 1x2 inches. Don’t stress over perfect shapes—rustic is great.
Return chicken to the pot: Add the shredded chicken back into the simmering broth. Keep heat at medium-low.
Cook the dumplings: Drop the dumpling strips into the simmering broth one at a time, stirring gently so they don’t clump.
Simmer for 12–15 minutes, stirring occasionally, until the dumplings are tender and cooked through.
Thicken if needed: For a creamier, slightly thicker broth, whisk 1 tablespoon cornstarch or flour with 2 tablespoons cold water. Stir into the pot and simmer 2–3 minutes until it gently thickens.
Finish and serve: Taste and adjust salt and pepper. Sprinkle with chopped parsley if you like.
Serve warm in deep bowls.