Heat olive oil in a large pot or Dutch oven over medium heat.
Add cremini, shiitake, and oyster mushrooms and cook until softened and lightly browned, about 5-7 minutes.
Add leek and garlic and cook for another 2-3 minutes, until fragrant.
Pour in white wine and cook for 1-2 minutes, allowing the alcohol to evaporate.
Add cauliflower, zucchini, chicken stock, salt, and pepper. Bring to a boil, then reduce heat and simmer for 20-25 minutes, or until the cauliflower is tender.
Use an immersion blender or transfer to a regular blender to blend the soup until smooth and creamy.
Taste and adjust seasoning as needed.
Serve hot.