Preheat the oven to 180C fan, 200C regular oven.
- You will need a large pie dish or rectangle baking pan. Brush it with melted unsalted butter.
- To make the filling, toss the grated zucchini with the teaspoon of salt and leave in a colander to drain for at least an hour. Give it a shake and toss from time to time. Then take handfuls of the zucchini and squeeze out as much liquid as you can, or wring it out in a tea towel.
- Lightly beat the eggs in a large bowl with plenty of pepper. Stir in the feta, mozzarella, rice or burghul and mint. Then add the zucchini and keep the mixture in the fridge until required.
- To assemble the pie, lay 10 sheets of filo on a tea towel, cover them with a dry tea towel and then with a damp tea towel. Keep the filo covered as you work to prevent it becoming dry.
- Use a wide pastry brush to melted unsalted butter on the filo sheets and work as quickly as you can.
- Arrange 5 sheets individually brushed into the baking dish so that the ends hang over the sides.
- Tip the zucchini mixture into the filo-lined dish and spread out evenly. Fold the overhang in over the filling. Brush the remaining sheets of filo with unsalted butter as before and place over the filling.
- Brush melted butter on top. Tuck the surplus filo snuggly in around the pie.
- Score the top couple of sheets of filo with a sharp knife in a diamond pattern or into segments where the pie is to be cut later. Make air vents by plunging the knife right through the top layers a few times. Sprinkle the top with sesame seeds.
- Bake the pie on a tray in the middle of the oven for one hour or until crisp and golden. Keep an eye on your first version so that it doesn’t burn.
- Rest the kolokithopita for 20 to 30 minutes before serving. Cut into slices and serve warm or at room temperature.