Bring about an inch of water to a boil in a medium saucepan. Add potato slices, reduce heat to simmer, and cook for 4 minutes, or until just softened. Remove from pan immediately and rinse with cold water. Once potatoes are cool, squeeze out any excess liquid and set aside.
Add walnuts to food processor and pulse until finely ground. Add olive oil and salt and pepper to taste; pulse until well-combined.
Spray a small skillet with cooking spray (I use olive oil in a mister) and heat at medium. Add mushrooms and sauté about 7–8 minutes, or until just beginning to brown. Season with salt and pepper.
Spread walnut mixture onto naan (it will be crumbly, but pressing it onto the naan will help it stick). Add half of the grated cheese, a layer of potato slices, the remaining cheese, and the mushrooms. Bake in oven for 8–10 minutes or until naan is crispy on edges and cheese has melted. Drizzle each pizza with ½ teaspoon of truffle oil just before serving.
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