Remove skin and excess fat from chicken pieces and transfer to a large dutch oven. Place peppercorns, bay leaves and allspice berries on a piece of cheesecloth and secure with a string and deposit it into the pot with the chicken. Add chicken broth to cover the chicken, cover the pot with a tight fitting lid and place the pot over medium high heat and bring to a boil. Reduce heat to a simmer and cook until the chicken pieces are cooked through, about 20 minutes. Using tongs, transfer the chicken to a cutting board to cool.
Set a fine mesh sieve over a large bowl and pour the broth through the sieve to remove the bouquet garni and any gray matter or other scum. Discard. If the pot still contains particulate, clean the pot and return it to the stovetop over medium high heat. When the pot has heated up, add butter, when it foams add the mushrooms and cook in a single layer until browned about 3-4 minutes. Flip to brown the other side. Pour the chicken broth over the mushrooms and add the chopped carrots, celery and onion. Bring the broth to a boil and reduce heat to simmer until vegetables are tender, about 15 minutes.
While vegetables are cooking, remove the meat from the chicken bones, discarding any fat, gristle, skin etc. Shred or cut the meat into bite sized pieces.
When the vegetables are tender, add the chicken pieces into the pot and stir well. Season with salt and pepper to taste.
Place 1/2 cup noodles in each bowl. Ladle chicken soup over the noodles. Sprinkle with parsley and serve.