Cut the onion in half. Mince one half and slice the other. Trim and separate shimeji mushrooms. Divide broccoli into small florets and microwave for 2 minutes.

Mix breadcrumbs and milk in a bowl to soften.

Microwave minced onion for 1 minute, cool, and mix with ground meat, egg, salt, pepper, and softened breadcrumbs. Shape into two patties.

Heat salad oil in a pan over medium heat, cook patties until browned on both sides. Cover and cook on low heat for 8 minutes. Remove from pan.

In the same pan, melt butter over medium heat. Add sliced onion and sauté until translucent. Add shimeji mushrooms and cook until coated in butter.

Add flour to the pan and cook until no longer powdery. Pour in water, cover, and simmer for 3 minutes.