In a bowl beat the eggs well, add milk and stir.
Place the first puff pastry sheet in a greased baking pan so as to cover the inner walls and brush it with oil and butter.
Pour the egg and milk mixture over the puff pastry sheet and spread the cheeses on top of it. Close the pie with the second sheet and coat it with oil and butter. You can also brush it with egg.
Sprinkle the pie with a little water and bake it in a preheated oven at 180ºC (356ºF) for about 1 hour.