In a medium sauce pan on medium heat melt butter. Once it's bubbly, add mushrooms and cook down until browning.
Add water or vegetable stock, salt and pepper. Bring to a simmer.
In a bowl add coconut milk and whisk in flour until fully combined
Add the flour and coconut milk to the simmering pot. Stir this constantly while you add. Cook this until it gets thick enough to coat a spoon.
This mix can be turned into a thinner cream of mushroom soup by adding 1 cup of water to the thickened mixture.