In a large pot or Dutch oven, combine chicken broth, celery, onion, and chicken breasts. Bring to a boil, then reduce heat to low and simmer partially covered for about 15 minutes, or until the chicken is cooked through.
While the chicken cooks, prepare the dumpling dough. In a medium bowl, whisk together flour, baking powder, and salt. Gently stir in the milk until the dough comes together into a shaggy ball.
Place dough onto a lightly floured surface and roll it out to about ¼-inch thick. Using a pizza cutter or knife, slice the dough into strips or squares (approximately 1–2 inches wide).
When chicken is fully cooked, remove from broth and set aside on a cutting board. Discard celery pieces and onion from the broth.
Drop dough strips carefully into the simmering broth, stirring gently. Simmer dumplings for approximately 20–30 minutes, stirring occasionally, until dumplings are cooked through and broth thickens to a gravy-like consistency.
As dumplings cook, shred or chop the cooked chicken into bite-sized pieces. Return the chicken to the pot, mixing gently to combine.
Season with salt and pepper to taste. Serve warm, and enjoy.