In a large, heavy skillet, melt the butter over medium-high heat. Add the mushrooms, shallots, salt and pepper, and sauté until soft and most of the mushroom liquid has evaporated, about 8 minutes. Add the chicken stock, cream and thyme, and simmer until the liquid has reduced by 50 percent in volume, about 5 minutes. Remove from the heat and stir in the truffle oil.
Place 2 potato crisps on each of 4 serving plates. Spoon 1 generous tablespoon of mushroom filling on top, topped with 1 teaspoon of grated Asiago. Continue layering the napoleon so that you have 3 layers of potatoes and 3 layers of mushrooms in all, ending with mushrooms on top. Garnish the top of each napoleon with 3 slices of truffle, and sprinkle of Asiago. Arrange the arugula around the outer edge of the plate and serve.
Yield: 4 servings