Melt the butter, roast the flour and slowly add 1/3 of the milk, stirring. Add the remaining milk, a little salt and freshly ground pepper. Stir until it thickens. Take it down from the fire and add 1 egg.
Place the pastry sheets at the edges of a baking pan, creasing the sheets but not in the center, so that they hold the stuffing.
In a bowl, mix all the cheese types with your hands.
Spread them all along the pie base.
Pour the bechamel evenly all over the pie. Slightly stir with a fork, making sure not to penetrate the base.
Add the top sheets in the same way as the base. Press them slightly so as not to get stuck between them.
Add olive oil and smear it with a cooking brush.
Bake the pastry in a preheated oven at 170°C, with extra heat on the top and bottom oven elements and air, until golden brown.
Leave it to cool down for 10 min, cut and serve.