Sprinkle the chicken breasts with salt, pepper, and paprika. Heat the oil over medium-high heat in a 3½-quart braiser. Add the chicken and cook, turning as needed, until the chicken is brown on all sides.
Add the broth to the pan. Bring to a boil; reduce heat. Cover and simmer 10 minutes. Add the celery, carrots, leeks, and onion. Return to a boil; reduce heat, and simmer for 10 to 15 minutes or until the vegetables are tender but not mushy and the chicken is done.
Meanwhile, make the dumplings: In a mixing bowl, combine the flour, baking powder, pepper, and the 2 tablespoons parsley. Using a pastry blender, cut in the shortening until the mixture resembles coarse crumbs. Add the milk; stir until combined. Gather into a ball and knead against the bowl a couple of times. Then, cut the dumplings into 12 pieces, and roll each piece into a ball.
Use a slotted spoon to transfer the vegetables and chicken to a bowl; cover to keep warm. Bring the broth to simmer and drop the dumplings into it. Cover and simmer about 15 minutes or until they are puffed and cooked through (a toothpick test works here).
Meanwhile, shred the chicken into 1 to 2-inch pieces.
After the dumplings are finished return the veggies and chicken to the braiser (scoot the dumplings around so that they stay on top of everything else). Cover and heat through.
Serve in shallow bowls, with three dumplings per person for hearty appetites; two dumplings for lighter appetites.
Recipe by Wini Moranville at http://chezbonnefemme.com/chicken-and-dumplings-in-your-braiser/