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) and all the fresh herbs. Bring the mixture to a simmer and let it cook covered with a lid 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. You might need to add some more salt.

Allow the soup to cool until it's cold enough to handle. Using a stick blender or a regular blender, blend the soup until you achieve your desired consistency.

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