Lay one sheet of filo pastry over a 20 cm diameter loose bottomed flan dish and brush with a little olive oil. Lay a second sheet at 90 degrees over the first and brush again with olive oil. Repeat with the third sheet. It is important to work quickly with the filo pastry so that it doesn't dry out. Keep the filo sheets wrapped until you are ready to use them and wrap any unused sheets straight away so that they don't dry out.
To prepare the filling
Lightly steam the broccoli florets and set aside.
Slice the leeks and mushrooms and cook gently in olive oil until soft.
Spoon the broccoli, leeks and mushrooms into the pastry case, and arrange evenly. Slice the cheese and arrange on top of the vegetables.
Fold the edges of the pastry part way over the filling, one sheet at a time, leaving an uncovered area in the centre. Brush any dry areas with olive oil.
To bake
Preheat the oven to 180°C, 350°F, gas mark 4
Bake in the centre of the oven until the pastry is golden and the cheese has melted. This is likely to take around 15 to 20 minutes, but check regularly to make sure the filo doesn't become overcooked. If the filo looks to be cooking too quickly cover any localised areas with foil and return to the oven.