Step 1

Heat oil in a large Dutch oven or other heavy pot over medium-high. Arrange mushrooms in a single layer and cook, undisturbed, until browned underneath, about 3 minutes. Stir and continue to cook, tossing occasionally, until golden brown all over, 5–7 minutes longer. Using a slotted spoon, transfer mushrooms to a plate, leaving oil behind.

Step 2

Add onion and shallots to pot; season with salt. Cook, stirring often and reducing heat as needed if beginning to brown, until very soft, 8–10 minutes. Add garlic and continue to cook, stirring occasionally, until softened and fragrant, about 3 minutes. Add wine and cook until almost completely evaporated, about 1 minute. Add 5 cups water and return mushrooms to pot. Bring to a simmer.

Step 3

Transfer 2 cups soup (including some mushrooms) to a blender and add cashews and miso. Purée until very smooth. Stir back into soup. Simmer, stirring occasionally, until flavors have melded, 10–15 minutes. Season with salt and pepper.

Step 4

Bring oil, garlic, thyme, and pepper to a simmer in a small saucepan over medium heat. Simmer gently until garlic is tender and just turning golden around the edges, about 3 minutes. Season with salt.

Step 5

To serve, ladle soup into bowls and drizzle with garlicky oil.