1. The first step in making chicken and dumplings is to cook the chicken. Place it in a Dutch oven and cover with water. Bring to a boil, and add salt, pepper, and any other seasonings called for in the recipe. Cover, reduce heat, and simmer for 1 hour.
2. Let the chicken and the broth cool. Skim the fat from the broth in the pan, remove the chicken from the pan, and bring the broth to a simmer.
3. Remove the skin from the chicken, then remove the chicken from the bones and shred the chicken with your fingers. Add the chicken and seasonings to the broth in the pan, and return to a simmer.
4. To make the dumplings, combine flour and poultry seasoning in a bowl. Cut in shortening and bacon drippings with a pastry blender until mixture is crumbly. Add milk, and stir until the dry ingredients are moistened.
5. Turn the dough out onto a floured surface. Roll it out to a 1/8-inch thickness, and cut into 1-inch pieces.
6. Bring the broth to a boil. Drop dumplings, a few at a time, into the boiling broth, stirring gently. It’s important that the liquid is boiling—otherwise the dumplings will become soggy. Reduce the heat, cover, and simmer for 25 minutes, stirring occasionally. Covering the pan will help keep the dumplings from deflating.