Cut the onion into wedges, quarter the shiitake mushrooms, and separate the shimeji mushrooms.

Trim excess fat from the chicken thigh and cut into bite-sized pieces. Season with salt and pepper.

Heat butter in a pot over medium heat. Add chicken and cook until browned. Add onion, shiitake, and shimeji mushrooms, and sauté until vegetables soften.

Add flour and stir until no dry flour remains. Pour in water, bring to a boil, and simmer covered on low heat for 8 minutes.

Add milk, salt, and pepper. Cook over medium heat for 2 minutes, stirring occasionally, until thickened.