Heat the olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Add the chopped mushrooms and cook without stirring for 3-4 minutes to allow them to brown. Stir occasionally and continue cooking until all the moisture has evaporated and the mushrooms are deeply caramelized (about 10-12 minutes).

Add the diced onion to the pot and sauté until softened and translucent, about 5 minutes. Stir in the minced garlic and dried thyme, cooking for one additional minute until fragrant.

Sprinkle the flour over the cooked mushrooms, stirring constantly for 1 minute to create a roux. This will help thicken the soup.

Slowly whisk in the vegetable broth, scraping up any browned bits from the bottom of the pot. Bring the mixture to a gentle simmer and cook for 5 minutes, allowing the soup to thicken slightly.

Stir in the full-fat coconut milk and the optional miso paste until completely combined and heated through (do not allow it to boil vigorously after adding the coconut milk). Season generously with salt and pepper to taste.

For a smoother texture, use an immersion blender to blend about half of the soup directly in the pot, leaving some textural chunks. Alternatively, blend in batches using a standard blender. Return all soup to the pot.

Ladle the hot soup into bowls, garnish with fresh chopped parsley, and serve immediately.