Add two quarts of water to a Dutch oven and add two teaspoons of salt and the chicken. Cover and bring to a boil.
Once boiling, reduce heat to a simmer and add pepper, celery leaves, and whole onion. Simmer until chicken is tender, about an hour.
Remove chicken from pot to cool, strain the broth, and pull apart the chicken meat, discarding bones and skin.
Return the strained broth to the Dutch oven and bring to a boil.
In a separate bowl, whisk together flour, salt, and baking soda. Cut in shortening until pea-sized, then stir in milk to form a dough.
Turn dough onto a floured surface, knead for a few minutes, then roll out to half-inch thickness and cut into squares.
Spoon dumplings into boiling broth, cover, and cook for ten minutes. Stir in chicken and heat through.
