Finely chop the onion, carrot, and broccoli. Separate the shimeji mushrooms into small clusters.

In a bowl, mix the ground meat, breadcrumbs, milk, salt, and pepper until well combined.

Shape the meat mixture into small patties.

Heat salad oil in a pan over medium heat and cook the patties until browned on both sides. Remove and set aside.

In the same pan, add butter and sauté the chopped vegetables until slightly softened.

Return the patties to the pan and add water, ketchup, Worcestershire sauce, sugar, salt, and pepper. Bring to a boil.

Reduce the heat to low, cover, and simmer for 15 minutes until the patties are fully cooked and the sauce thickens.