In a large Dutch oven set over medium-high heat, combine the chicken broth, shredded chicken, condensed soup, and poultry seasoning. Bring the mixture to a rolling boil, then lower the flame, cover the pot, and let it simmer gently for 5 minutes.
While the soup simmers, prepare the biscuit dough by patting or rolling six biscuits to approximately ⅛-inch thickness on a lightly floured work surface. Cut the flattened dough into narrow strips, about ½-inch wide.
Remove the pot’s lid and increase the heat back to medium-high to bring the soup back to a boil. One by one, gently drop the dough strips into the hot liquid, stirring softly to prevent them from clumping together. Once all the dumpling strips are added, stir in the chopped carrots and celery.
Reduce the heat again to low. Cover the pot and let the dish simmer for 20 minutes, stirring carefully every 5 minutes to ensure the dumplings cook evenly and don’t adhere to each other.
Portion the soup into serving bowls and garnish with fresh parsley if desired. Serve immediately.