Combine all mushrooms in a large pot with olive oil. Cook over medium heat until softened and browned, about 10-15 minutes.
Continue cooking the mushrooms, stirring occasionally, until they release their liquid and it evaporates. This will concentrate their flavor.
Increase the heat to high and continue cooking the mushrooms without stirring for 2 minutes. Stir and repeat this process 6 times to achieve a golden-brown color.
Transfer the mushrooms to a blender. Add a small amount of milk and blend until smooth. Add more milk as needed to reach the desired consistency.
Season with salt and pepper to taste.
Serve hot, garnished with a drizzle of aged balsamic vinegar.