Preheat the oven to 400°F (200°C). Cut the top off the garlic head, drizzle with olive oil, and wrap in foil. Roast for 30-35 minutes.
In a large pot, heat olive oil over medium heat. Add the onions and cook until translucent, about 5 minutes.
Add the mushrooms and thyme, cooking until softened, about 10 minutes.
Squeeze the roasted garlic cloves into the pot, then add the vegetable broth. Bring to a simmer.
Stir in the coconut milk and cook for 5 more minutes.
Use an immersion blender or regular blender to purée the soup until smooth.
Season with salt and pepper to taste, and garnish with parsley if desired.
Serve hot with crusty bread.