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Heat oven to 200C/fan 180C/gas 6. tip the mushrooms into a bowl and pour over boiling water to just cover them. Leave to cool, then drain (reserve the stock for another time), squeezing out excess liquid.
Heat about a fifth of the butter in a pan and stew the garlic over a low heat for 3-4 mins. Throw in the mushrooms and continue to cook for 15-20 mins until tender. Season well and set aside.
Peel and slice the potatoes (don't wash them, as the starch holds the cake together). Butter a 20cm ovenproof pan, then overlap a layer of potatoes on the bottom. Build up the cake with layers of potato, scatterings of mushroom, dots of butter and seasoning, finishing with a layer of potatoes. Cover with foil and bake for 50-60 mins, until a knife slides into the cake easily. Remove from the oven, run a knife around the outside to make sure it doesn't stick, then leave to relax for at least 5 mins. Carefully invert onto a baking tray, cool and keep in the fridge. To serve, heat in the oven until piping hot and cut into wedges.