Begin by poaching the chicken. Put the chicken in a large stockpot and cover with 1 gallon of cool water. Add the vegetables and herbs and bring the pot up to a boil over medium-high heat. Skim well; then simmer, uncovered, for 45 minutes, skimming frequently as the oil rises to the surface. When done, remove to a platter and set aside to cool. Strain the liquid and reserve it for use as chicken stock. Shred the chicken meat and discard the skin and bones.
Preheat oven to 325 degrees F.
Roughly chop the walnuts and then gently toast in a dry skillet over medium heat until they brown and are slightly fragrant. Season walnuts with salt once they are finished toasting. Add the walnuts, mayonnaise, mustard, lemon juice, celery, parsley, olive oil, and salt and pepper, to taste, in a large mixing bowl and combine. Fold in the shredded chicken and set aside while you prepare the bread.
Toast the bread in a hot oven until golden. Smear each piece with a little butter and then a tablespoon of cranberry sauce over 4 of the pieces. Lay the 4 cranberry-smeared pieces out on a sheet tray and top each piece with 2 to 3 slices of thick-cut brie. Pop this back in the oven for a minute or 2 so the cheese is slightly melted and creamy. Remove from the oven and top with a few slices of green apple. Top with a scoop of the chicken salad and cover with the other half of the bread to complete the sandwich. Serve.