Thinly slice the onion, and cut all the other ingredients into bite-sized pieces. Lightly season the chicken with salt and pepper.
Heat butter in a pot and sauté the onion over medium heat until it starts to wilt. Add the chicken, and once the surface turns white, sprinkle in the flour.
Add the carrot and briefly sauté. Sprinkle flour again (preferably sift it in). Incorporate with the ingredients as you continue to sauté over low heat.
Pour in the water and mix. It will start to thicken, so make sure to mix it well.
Once it starts to thicken, add the potatoes and shimeji, and mix.
Add the milk and consommé. Slightly increase the heat and continue mixing. Reduce to low heat right before it starts to boil.
Cover, and simmer for about 15 minutes until the vegetables soften, mixing the stew every once in a while. To finish, add heavy cream, and season with salt and pepper to taste.
If you're using kabocha squash, I recommend adding it for the remaining 10 minutes of simmering to prevent it from disintegrating into the soup.
Story Behind this Recipe
It's tastier than store-bought roux.
Adjust the creaminess of the soup with the amount of flour. The key is to mix it well with the ingredients using a spatula to prevent it from becoming lumpy. Do not allow it to boil once the milk is added. It's fine to omit the heavy cream, but it's recommended for more creaminess.