In a large mixing bowl, whisk together the flour, baking powder, and salt.
Add the cubed butter to the flour mixture. Cut it in with a fork, pastry cutter, or food processor until the mixture resembles coarse crumbs with pea-sized pieces of butter.
Pour in the milk gradually, stirring with a fork until the dough comes together. Use your hands to form the dough into a ball, dusting with extra flour if it feels sticky.
Lightly flour a large sheet of parchment paper or a clean surface. Roll the dough into a thin sheet, about 1/4-inch thick (thinner dumplings cook more evenly). Dust the top with flour, then cut the dough into small square or rectangular pieces, about 2 inches wide. The shapes do not need to be exact.
In a large Dutch oven, bring the chicken broth to a gentle boil over medium-high heat. Stir in the black pepper and adjust seasoning with additional salt to taste.
Working in batches, drop the dumplings into the boiling broth one at a time, stirring gently so they don’t stick together. The dumplings will puff slightly and rise to the top after a couple of minutes.
Add the cooked chicken to the pot, reduce the heat to medium-low, and let the mixture simmer for 15 to 20 minutes, stirring occasionally. The broth will thicken slightly as the flour from the dumplings cooks out.
Taste and adjust seasoning as needed. Serve hot.