Bring the broth to a boil in a large soup pot and season with the herbs. Add the carrots and celery and reduce to low. Cover the pot and simmer the vegetables while preparing the dough.

Combine the flour and salt, then cut in the shortening until the texture resembles grains of rice. Stir in the egg and hot milk, then turn out onto a lightly floured surface. Divide the dough in half. Roll each half very thin, approximately 1/8-inch in thickness. Cut into 1 to 1 1/2 –inch squares.

Bring the broth mixture back to a boil, and drop the pot pie squares in slowly. Once all are in the broth, stir to ensure the squares don’t stick together, then reduce the heat to a strong simmer. Cook 20 minutes, or until the pot pie dumplings are tender. Add the chunks of chicken and heat through. Taste for seasoning, adding salt and pepper as needed.