Heat the olive oil in a large soup pot. Sauté the chopped onions and leeks until softened (~3-5 minutes).

Add the mushrooms, minced garlic, salt, and pepper, and cook until they release their moisture and become golden brown (5 minutes). Stir constantly to avoid burning.

Add the diced potatoes, broth, and white wine (if using) along with all the fresh herbs. Bring to a simmer and let cook covered for about 15-20 minutes or until the potatoes are tender.

Remove the herbs from the soup. Stir in the grated Parmesan and heavy cream (if using), allowing it to melt into the soup.

Taste and adjust the seasoning, adding more salt if needed.

Allow the soup to cool until it's cold enough to handle. Blend the soup until you achieve your desired consistency using an immersion blender or regular blender.

Serve the soup hot, garnished with additional Parmesan, a drizzle of olive oil, and fresh herbs.