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Roll the pastry out on a floured surface and cut out 4 circles, about 15cm wide. Leave to chill on a lined baking tray in the fridge.
Heat oven to 200C/fan 180C/gas 6. Heat a large frying pan until hot, then add the butter and fry the mushrooms for 5 mins until there is no liquid left in the pan. Season, then take off the heat and mix mushrooms with the Parmesan, parsley and garlic.
Score a 1cm border around the edge of each tart, then spoon the mushrooms into the centre circle. Brush the edge with beaten egg, then bake the tarts for 20 mins until puffed up and golden. Serve immediately.