Mince half the onion and microwave for 1 minute at 600W, then cool. Slice the other half thinly. Trim and separate shimeji mushrooms.

Mix breadcrumbs and milk in a bowl. Add ground meat, minced onion, and seasoning ingredients. Knead until sticky.

Divide the meat mixture into two portions, shape into patties, and indent the center slightly.

Heat salad oil in a pan and sear patties for 2 minutes per side until browned.

Push patties aside, wipe the pan clean, add butter, and sauté sliced onion and shimeji mushrooms until softened.

Add all sauce ingredients except milk, stir, and simmer covered on low heat for 8 minutes.

Add milk and simmer on medium heat until slightly thickened.