Brown chicken in all sides in a little olive oil. Add 1 chopped onion, 2 chopped carrots, 2 chopped ribs of celery and some bay leaves. Sprinkle with salt and pepper. Cook until vegetables have softened then add 4 cups chicken stock and 4 cups water. Bring to a simmer, cook 30 minutes, covered, and turn off heat. Let stand 60 minutes, covered. Remove chicken to a cutting board, pick meat from bones and return it to the pot. Bring to a simmer. Rub 1/4 cup butter into 1/3 cup flour to make a paste. Add the flour paste in small bits to the pot, stirring often. Let simmer about 5 minutes. Stir together 2 cups flour, 1 tablespoon baking powder, 1 teaspoon salt, 2 large eggs and 3/4 cup buttermilk. Drop by spoonfuls into the simmering soup, cover and cook ten minutes.