Melt the butter in a pot and sauté the green onions (leave some for garnish), garlic, and thyme for 1-2 minutes. Then, add the mushrooms and cook for 3-4 minutes, or until the mushrooms soft. Add the flour and continue cooking for another minute, stirring constantly
Add the stock and miso and bring to a boil while stirring. Once boiling, reduce to low heat and simmer for 2 minutes, stirring occasionally.
Whip the heavy cream and whisk it into the soup. Stir the soup until it has a smooth, creamy texture. Season to taste with salt and pepper. Do not allow the soup to boil.
Serve and garnish with leftover green onions.