In a large stockpot or Dutch oven, melt butter over medium heat. Add celery, carrots, and onion, and saute until translucent.
Mix together salt, black pepper, garlic, and paprika. Rub over chicken. Add chicken to the Dutch oven and pour 4-6 cups of chicken broth over the top. (The amount of broth depends on whether you prefer more of a soup or a thicker, pot pie-like result. I use 5 cups.) Tie rosemary and thyme together with kitchen twine and drop into the broth. Add bay leaf. Bring to a boil, then reduce heat to low. Simmer for 30 minutes.
While chicken is cooking, in a medium bowl, mix together flour, baking powder, and salt. Cut shortening into the flour mixture with a pastry cutter or your fingers, until it is coarse crumbs. Remove 1 ½ cups of broth from the Dutch oven, and mix into the flour mixture a little at a time until a soft dough is formed.
Turn dough onto a floured surface and knead about 5 minutes, until it is soft, pliable, and smooth. Cover and let rest 10-15 minutes.
Once rested, place dough back onto a floured surface and roll out until it is ⅛-inch thin. With a sharp knife or pizza cutter, cut into 2"x1" strips.
When chicken is cooked through, remove it from the pot and cover with foil to keep warm. You can shred or leave whole. Remove herbs and bay leaf from the pot and discard.
Raise the heat of the broth to medium-high and bring to a boil. Once boiling, drop in dumplings once at a time, stirring occasionally, to keep them from sticking together. Cook for 10 minutes.