Combine flour, breadcrumbs, garlic, parsley, ½ tsp salt, and ½ tsp pepper in a bowl. Gradually add 1 cup cold water to form a firm dough.
Dice chicken into ½-inch cubes and simmer in broth for 10 minutes until just firm. Set aside.
Divide dough into four portions. Roll into ¼-inch thick rounds. Place 2-3 chicken pieces on each round, fold in half, and crimp edges with a fork.
In a large pot, bring broth to a gentle simmer. Add dumplings in a single layer. Cover and cook 12-15 minutes until golden.
Remove dumplings. Mix 1 tbsp flour with 2 tbsp water to create a slurry. Stir into remaining broth to thicken as a sauce for serving.