Place the chicken, broth, kosher salt, black pepper, and any optional onion, celery, or bay leaf in a large pot. Bring the liquid to a gentle boil, reduce the heat, and simmer for approximately 20–25 minutes, or until the chicken is cooked through.

Transfer the cooked chicken to a plate and let it cool slightly. If you used vegetables or a bay leaf, strain the broth, then shred or chop the chicken and set it aside.

Whisk the flour, baking powder, and kosher salt together in a mixing bowl. Cut in the cold butter or vegetable shortening until coarse crumbs form, then stir in the milk just until a soft dough comes together.

Turn the dough onto a lightly floured surface and knead it very briefly. Roll it to about 1/8-inch thickness, cut it into strips or small squares approximately 1 x 2 inches, and let the pieces rest for 10–15 minutes.

Bring the broth back to a gentle simmer. Add the dumplings a few at a time, stirring carefully between additions so they do not stick together, then cover and simmer for 15–20 minutes.

Stir occasionally while the dumplings cook, keeping the pot at a gentle simmer rather than a hard boil. They are ready when tender and the broth has thickened slightly.

Return the shredded chicken to the pot and simmer for 3–5 minutes so it warms through and absorbs some of the seasoned broth. Taste and adjust the salt and black pepper before serving.