In a large bowl, combine cold water (enough to cover the chicken breasts) and 2 tablespoons salt. Place the divided chicken pieces in the salted water (brine) and let stand for approximately 45 minutes. Remove the chicken pieces from the brine and rinse thoroughly under cold water. Slice each breast on the bias into 4 thin slices. Heat oil in a large skillet on medium-high heat. Pan sear the chicken about 1 minute on each side until golden. Remove from heat.
Melt 2 tablespoons of butter with 2 tablespoons of vegetable oil in a medium skillet on medium heat. Add the sliced shiitake mushrooms and saute until crispy. Remove the mushrooms with a slotted spoon and place them on a paper towel to remove excess oil. Season the mushrooms with salt and freshly ground pepper.
Cut a small hole in the middle of each raw potato slice for the rosemary "pick." Pour at least 2 inches of oil in a medium pot and heat until the oil begins to smoke. Carefully place the potato slices in the oil 2 or 3 at a time. Turn potatoes occasionally so they brown evenly. Remove the potatoes when they are tender/crisp and allow the excess oil to drain on a paper towel. Season, to taste, with salt.
Pour 2 cups of chicken stock into a medium pot. Add the chicken carcass, shiitake mushroom stems, marjoram and sage. Let simmer until reduced by 1/2. Strain the reduced stock with cheesecloth or a fine mesh strainer into a small saucepan and place on low heat. Add the gelatin from the pate to the pan and stir until it dissolves. Gently stir in 2 tablespoons of butter. Do not boil. Season, to taste, with salt and pepper.
Place a crispy potato slice on each plate. Top each potato with 1 slice of chicken. Spoon about 2 tablespoons of duxelle onto the chicken. Using a sharp knife, slice a thin piece of pate and place on top of the duxelles. Place a second potato slice on top of the duxelle and repeat the process for each plate. Top each stack with the third slice of potato. Secure the stack with a "pick" of rosemary (take a 4-inch piece of rosemary and gently remove the bottom 2 to 3 inches of leaves, leaving 1 to 2 inches of rosemary leaves on each pick).
Cook the shallots in butter in a medium sized pan, on low heat. Add the chopped mushroom to the shallots and season with salt and pepper. Cook until the mushrooms render liquid. Remove from the pan and puree the mixture in a food processor.
Return the pureed mushroom mixture to the pan. Add heavy cream. Reduce the cream until the mixture is pasty.
Remove from heat and add parsley and thyme. Season with salt and pepper, to taste.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.