In a large soup pot, heat 2 tablespoons of olive oil over medium heat. Add the chopped yellow onions and white parts of the leeks, cooking for about 3-5 minutes until they soften and become translucent, releasing their sweet aroma.

Stir in the chopped brown mushrooms and minced garlic, enhancing the mixture with a pinch of salt and black pepper. Cook for another 5 minutes, stirring frequently, until the mushrooms become golden and tender.

Add diced potatoes, vegetable broth, and dry white wine (if using) to the pot. Toss in the fresh herbs, ensuring they are evenly distributed. Increase the heat to bring the mixture to a gentle simmer. Cover the pot and allow it to cook for 15-20 minutes, until the potatoes are fork-tender.

Once the potatoes are cooked, remove the fresh herbs if desired, then stir in the grated Parmesan (or nutritional yeast for a vegan option) and heavy cream (or plant-based cooking cream). Allow the cheese to melt into the warm soup before blending.

Use an immersion blender to achieve your preferred consistency, making it smooth and creamy. Taste and adjust the seasoning with more salt and pepper if needed. Ladle the warm soup into bowls and garnish with extra Parmesan, a drizzle of olive oil, and a sprinkle of fresh herbs.