Slice the leeks into rings and finely chop the spring onions. Add the olive oil into a large pan and sauté the leeks and onions for a few minutes, so they may wilt a little. Strain in a strainer and leave to the side so that the temperature drops. Then, place in a bowl.
Beat the egg with a fork and add to the bowl with the leeks and spring onions, continuously mixing. Add the cornstarch, dried mint, salt and pepper.
Crumble the feta cheese with your hand and add to the bowl.
On low heat, melt the butter. Butter a 30x35cm pan and place one sheet of fyllo dough; cover the remaining sheets with a towel to prevent them from drying
Add three more fyllo dough to the first one, buttering the sides of each one with a cooking brush. Pour half the filling and place a wrinkled fyllo dough sheet on top. Butter the sides of the fyllo dough and add the remaining filling.
Fold the protruding fyllo dough sheets downwards. Place the remaining four fyllo dough sheets on top of the filling, buttering the sides of each one and folding the edges so that they do not protrude. Finally, butter the surface of the last sheet.
Bake in a preheated oven at 180 degrees Celsius for 15 minutes with bottom heating and then switch to top-bottom heating for another 30-40 minutes (time depends on the oven), until golden brown. If your oven does have the option of bottom heat, use top-bottom heat from the beginning.