In a large stockpot, heat oil over medium heat. Add leeks, onions, one teaspoon salt, 1/2 teaspoon black pepper, thyme, and bay leaves. Cook until onions and leeks are soft, about five minutes.

Add garlic and cook for 30 seconds. Add mushrooms and cook until very soft and browned, 10–15 minutes.

Add wine and cook until most of the liquid has evaporated, about four minutes. Add broth and bring to a simmer.

In a bowl with high sides (to avoid splatter), use an immersion blender to purée the almond milk and beans until smooth. Stir in vinegar, and add this mixture to the soup. Cook about five minutes.

Transfer 1/3 of the soup to a separate pot or other container and blend until smooth. Pour blended soup back into the stockpot and stir to combine over low heat. Simmer for five minutes. If the soup is too thick for your liking, add a bit of water.

Season with extra kosher salt and black pepper, as needed. Serve warm, with croutons, thyme, and a drizzle of truffle oil.