Boil whole chicken in 8 cups of water, salt and pepper for approximately 40 minutes until chicken is falling off bone. Remove hen from broth, skin and debone. Set aside. Keep broth on the stove on warm.
Mix eggs with 1 cup of flour and slowly add flour until dough becomes stiff. You may add a tablespoon of water at a time if dough gets too stiff to work with. Flour dough and roll in a rectangle. Roll the dough up like a jelly roll from the short side and slice into 1/2" slices. Turn heat up on the broth to return to a boil. Unroll and drop dumplings one at a time into boiling broth to prevent them sticking together. Cook until done (about 5-7 minutes). Return chicken to broth. Turn heat to low and allow chicken to heat to broth temperature by simmering for 60 minutes. You may add small amounts of water if needed.