Put the chickpea miso and 4 cups of water in a high-speed blender (or replace the miso and water with vegetable broth). Add the nuts and process until creamy. Set aside.
Heat 2 tablespoons of the oil in a large, heavy pot over medium heat. Add the leek, onion, garlic, and thyme, along with a few pinches of salt, and cook, stirring now and then, until softened but not browned, 8 to 10 minutes.
Add the remaining tablespoon of oil and mushrooms to the pot, stir to combine with the leek mixture and cook until the mushrooms begin to release their liquid, 5 to 6 minutes. Add the reserved creamy broth mixture to the pot and turn the heat up to medium-high. Once the soup begins to boil, lower the heat and simmer for 15 minutes. Stir in the lemon juice.
Use a hand held stick blender to process the soup until it’s creamy and well blended. (Note: If you do not have a hand held stick blender, allow the soup to cool and then puree in several batches in blender.) Serve warm or cold.
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Be sure to buy a chickpea-based miso, not a soy-based one for this particular soup recipe. I like Miso Master brand organic chickpea miso. Just like soy miso, chickpea miso is sold as a paste in the refrigerated section of natural food stores.