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 hr.
Remove the chicken to a separate bowl.
For the dumplings, combine the flour and butter until the pieces are 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, and cut into squares.
Bring the broth back to a boil. Drop the dumplings in one-by-one. Once they’ve all been added, bring back to a boil, lower the heat and simmer/thicken for 10 minutes.
Pull apart the chicken, and add your desired amount to the pot. Add additional salt and pepper to taste.