Add chicken and broth to a Dutch oven or large pot. Bring to a boil, then reduce heat, cover, and simmer for 20 minutes.

Meanwhile, make the dumplings: pulse flour, salt, baking powder, and cold butter in a blender or food processor until mixture resembles fine sand.

Transfer to a bowl, make a well, add milk, and gently stir with a fork until a shaggy dough forms.

Roll dough on a floured surface to ¼-inch thickness. Cut into 1-inch squares and dust with flour to prevent sticking.

Remove chicken from the pot, shred, and return it to the broth.

Bring the broth back to a gentle boil. Add the dumplings a few at a time, stirring between additions to prevent clumping.

Cover, reduce heat to a simmer, and cook for 25–30 minutes, stirring occasionally, until dumplings are tender and cooked through.