Heat a large dutch oven pot over medium high heat. Add in olive oil and heat through, 1 minute. Add in celery, carrots, and onion and saute 5 minutes, or until onions are soft and translucent. Stir in garlic and cook 1 minute more.
Add in chicken breasts and season with salt and pepper. Pour in chicken broth and milk. Bring to a boil and boil 20 minutes, or until chicken is cooked through and easily shreds with a fork.
Meanwhile, make the dumpling dough. Mix flour, baking powder, and salt in a mixing bowl. Cut in the cold shortening using a pastry cutter or food processor. Gradually pour in the buttermilk, stirring until the dough comes together. Turn the dough out on a floured surface and work it just until everything is well combined. Roll the dough out about 1/4-inch thick. Cut into 1 inch strips. Cut each of those strips into pieces that are approximately 2 inches in length.
Shred chicken directly in soup pot, or remove to a cutting board, shred, and return to soup. In a small bowl, whisk together cornstarch and water. Pour into soup pot, stir in, and return to a simmer.
Drop strips into the soup and simmer 15-20 minutes. Serve hot.