Dice the eringi mushrooms into 5mm pieces. Slice green beans diagonally into thirds. Finely chop the onion and microwave for 1 minute at 600W to soften, then let cool.

Mix melted butter and flour in a bowl. Gradually add milk while stirring to create a smooth mixture.

In a separate bowl, mix milk and breadcrumbs until softened. Add ground meat, onion, salt, and pepper, then mix until sticky. Divide into two portions and shape into oval patties with a slight indentation in the center.

Heat salad oil in a frying pan over medium heat. Cook the patties until browned on both sides. Add diced mushrooms and water, bring to a boil, and simmer for 5 minutes while skimming off any foam.