1. Heat 1/3 cup olive oil in large pot. Add sliced leeks with a sprinkle of salt and sauté over low heat for 15 to 20 minutes, until soft and translucent. Add garlic and Jerusalem artichokes and sweat over low heat for another 30 minutes. Add water until the artichokes are just covered, along with thyme. Bring to a boil, then reduce heat and simmer until artichokes are fork-tender.
2. Transfer to Vitamix or food processor. (Don’t use a hand blender for this. So much of this soup is its creaminess, which you can’t quite achieve with a hand blender.) Blend for at least five minutes while drizzling in a bit more olive oil, until you get that perfect velvety texture. Season with salt to taste.
3. To make the apple chips: Preheat oven to 300 degrees Fahrenheit. Using a mandoline, thinly slice apples widthwise (across the center). Gently place apple chips directly on the oven rack and cook for 15 to 20 minutes, until dried out. Remove from the oven and let sit to crisp up. Apple chips can be made a day in advance and left at room temperature.
4. To prepare the mushrooms: Heat one tablespoon olive oil in a large skillet. Add mushrooms and sprinkle with salt. Sauté for 15 minutes, until soft.
5. Serve soup in shallow bowls, topped with mushrooms and apple chips. Drizzle with a little olive oil and finish with chopped parsley.