Place chicken in a large pot. Add salt and pepper, a dash of cayenne, a bay leaf, and a handful of celery tops. Cover with water and cook until done. Discard bay leaf. Add vegetables, and continue cooking until vegetables are nearly done.
Meanwhile, make the dumplings. Mix together flour, 1/2 teaspoon salt, baking powder, chicken fat. Mix in enough water to make a stiff dough. Divide dough into three parts. Roll out and cut into squares.
Add 1/3 dumplings to simmering chicken and cook 5 minutes. Add another third and cook 5 minutes more. Add the remaining third and cook 5 minutes longer. Serve.