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Heat 1 tbsp of the butter and the oil in a large pan and fry the mushrooms for 10-15 mins until golden. Stir in the green beans and cook for another 3-4 mins until the beans turn bright green. Scoop out the veg onto a plate.
Heat the oven to 200C/180C fan/gas 6. Melt the remaining butter in the pan until foaming. Remove from the heat briefly and sprinkle over the flour, stirring into the butter to make a golden brown paste. Return to the heat and add the milk, a splash at a time, continually stirring until all the milk has been added and you get a smooth, thick white sauce. Season well. Stir the beans and mushrooms into the white sauce, and spoon into a medium ovenproof dish.
Scatter over the crispy onions, then bake for 20-30 mins until bubbling and golden, covering if the onions brown too quickly.