To a large stockpot on medium-high heat, add chicken, broth, water, and seasonings. Add enough water to nearly cover the chicken. Bring to a boil, then lower the temperature to medium-low. Cover and simmer 1 hour.
Carefully transfer the cooked chicken to a bowl.
For the dumplings, in a bowl, whisk together the flours.
Grate butter into the flour and toss until coated.
Make a well in the center and add milk. Fold the ingredients until it forms a cohesive dough ball. If it seems too dry and won’t combine, add additional milk.
Turn the dough onto a floured surface. Roll to an ¼ inch thickness.
Using a butter knife or pizza cutter, cut into your desired size squares. Optional step, sprinkle cornmeal on top of the dough and gently pat.
Bring the broth back to a boil. Drop the dumplings in one-by-one. Once they’ve all been added, bring the mixture back to a boil. Lower the heat to low and simmer until the dumplings have cooked and the mixture has thickened, about 10 minutes.
Pull apart the chicken, and add your desired amount to the pot. Add additional salt and pepper to taste. See “Pro Tips” for thickening suggestions, if desired.