Remove the stalks of the spinach, wash and chop roughly.
Mix together in a bowl with the feta cheese, shredded mozzarella and two of the beaten eggs.
In a separate bowl, mix the water, 1 tablespoon olive oil and milk.
Grease a rectangular baking dish with the remaining olive oil.
Lay the pastry sheets along its long side and cut in half vertically.
Open the sheets only when you are ready to use them and cover the rest with a damp towel so that they don’t dry out.
Lay three sheets in the greased baking dish.
Pour a little of the milk-olive oil-water mixture (about 3 tablespoons) all over the sheet.
Repeat this layering two more times, using three fillo sheets each time.
Lay three more sheets over and spread the spinach filling evenly.
Continue laying three sheets of fillo, pouring over each the milk mixture, three more times.
Lay the remaining sheets on the top of the pie, sprinkling the milk mixture.
Whisk together the remaining beaten egg with a little olive oil and brush over the pastry.
Sprinkle with sesame or nigella seeds.
Bake the pie in the oven for about 40 minutes, until the top is golden brown.
Serve hot, cut into pieces.
This dish can be successfully reheated.