Hen: 1. Put the chicken, neck, gizzard, and heart in a 6-quart heavy pot. Cover with 3 quarts cold water and bring to a simmer over high heat. As the water approaches simmering, begin to skim away any fat or scum. Reduce the heat to medium and simmer for 5 minutes while continuing to skim. Add 1 of the carrots, 1 of the celery stalks, the onion, garlic, bay leaves, 1 tablespoon salt and the peppercorns. Reduce the heat to low, cover, and simmer for 10 to 15 minutes.
2. Transfer the chicken to a cutting board. After letting it cool for a few minutes, cut off the breast meat, which ideally should be just done and still slightly pink at the bone. Set the meat aside and return the rest of the chicken to the pot. Simmer gently for 20 minutes over low heat. Add the dark green top of the leek and the parsley stems to the pot, and simmer for 10 minutes.
3. While the chicken is cooking, dice the remaining 2 carrots and 2 celery stalks.
4. Remove the legs from the chicken and reserve. Remove other meat. Strain the broth. You will have about 2 quarts. Discard the vegetables and bones. Rinse out the pot and pour the broth back into it (off the heat).
5. When the chicken legs are cool enough to handle, remove the skin and pick the meat off the bone. Gently tear it into bite-size chunks. Repeat with the reserved breast and other meat, and set all chicken meat aside.
6. Bring the broth to a boil over high heat and add the diced carrots, celery, leek and the wine. Reduce the heat to medium and cook for 4 minutes until the vegetables are slightly softened. Add the cream and chicken and bring back to a simmer. Check the seasoning and adjust as necessary.
Dumplings: 1. Whisk together the flour, baking powder, and salt in a medium bowl. In a small bowl, whisk the eggs, buttermilk and butter. Add the wet ingredients to the dry. Mix well with a wooden spoon, and then stir in the parsley and chives.
2. Using 2 teaspoons, form dumplings (I used my hands to roll them into balls) and drop them into the simmering stew, spreading them out. Toward the end of the process, the pot may begin to seem crowded; give it a gentle stir as necessary. When all the dumplings are in the stew, give it another stir, flipping over any dumplings that are not submerged. Cover and simmer for 5 minutes.
Garnish: Remove stew from the heat, stir in the parsley and the chives, and serve with freshly ground pepper.
Yield: 6 to 8 servings, with leftovers.
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