In a large soup pot, melt the vegan butter over medium-high heat. Add the mushrooms, onion, and garlic and sauté until the mushrooms have softened and browned. Sprinkle over the flour, stir in, and cook 1 minute more.
Pour in the vegetable broth, coconut milk, thyme, salt, pepper, and nutmeg. Use your spoon to scrape the bottom of the pan and remove any bits stuck to the bottom. Bring to a simmer and cook for about 5 minutes, to thicken slightly.