Wrap bay leaves, fresh thyme, parsley, and black peppercorns in a piece of cheesecloth, and tie into a sachet with kitchen twine. Set aside. Heat butter and olive oil in a large saucepan over medium heat. Add leeks and onion, and cook until soft, about 20 minutes. Add garlic, and cook 2 minutes more. Add potatoes, celeriac, squash, and pear, if using. Cover, and cook over medium heat for 5 minutes. Add sachet, chicken stock, salt, and black pepper. Bring to a boil, and reduce to a simmer. Cook until vegetables are soft, about 20 minutes. Remove sachet, and discard. Pass the mixture through a food mill into a medium bowl in several batches. Add heavy cream or milk, if desired. Bring soup just to a simmer over medium heat. Taste, and adjust for seasoning. Garnish with parsley. Serve immediately.
Place peppercorns, dill, parsley, bay leaves, leeks, carrots, celery, chicken, wings, and backs into a large stockpot. Add stock and 6 cups cold water. Bring to a boil. Reduce to a very gentle simmer, and cook for 45 minutes. Liquid should just bubble up to the surface. A skin will form on the surface of the liquid; skim this off with a slotted spoon, and discard. Repeat as needed. After 45 minutes, remove chicken from the pot, and set aside until it is cool enough to handle. Remove the meat from the bones, set the meat aside, and return the bones to the pot. Shred the chicken, and set aside in the refrigerator until ready to use. Continue to simmer the stock, on the lowest heat possible, for 3 hours, skimming as needed. The chicken bones will begin to disintegrate. Strain the stock through a fine sieve into a very large bowl. Discard the solids. Place the bowl in an ice bath, and let cool to room temperature. Transfer to airtight containers. Stock may be refrigerated for 3 days or frozen for 4 months. Refrigerate for at least 8 hours, or overnight. If storing, leave fat layer intact to the seal the stock. Before using, remove the layer of fat that has collected on the surface.
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