Heat the oil in a pan over medium heat and cook chicken on both sides until they change color and smell good.
Add all vegetables and stir fry until they are coated evenly. Pour wine and water in it and simmer over medium heat until the vegetables soften.(for about 15 mins) Skim off the foam when it rises on the surface.
Turn off the heat and add stew roux and lightly stir. Let it stand for a while.(for about 5 mins) Add milk and simmer again with low heat until thickened. Keep stirring from time to time not to make it burned.
Add miso, cheese and butter last. Season with salt and pepper. Stir gently to mix. Sprinkle with parsley for topping.