First, crumble the kefalograviera and feta cheese in a bowl. In another bowl whisk the eggs. Add the milk mixture, oil, pepper and salt and stir well.
Lightly butter a baking pan and lay 2 sheets on the bottom, lightly buttering each one. Place the ¼ of egg mixture and a little quantity of the cheeses, and cover with the second sheet. Repeat the procedure with another two layers of phyllo sheets. Then turn the edges of the sheets and lay the last one and drill it with a fork. Add the rest of the mixture of eggs and cheese.