Melt 6 tablespoons butter in small saucepan over medium-low heat. Whisk in the flour until smooth and cook, stirring constantly, for 2 minutes. Gradually pour in the milk, stirring constantly with a whisk or wooden spoon. Add the salt and nutmeg, stirring occasionally, until mixture is bubbly and thickened, 5 to 10 minutes.
Mash the feta cheese with a fork in a bowl and stir in the grated kefalotiri, beaten eggs and parsley. Pour in the hot white sauce and mix well.
Preheat oven to 180 C / Gas 4. Butter a 23x33cm baking dish.
Line the buttered baking dish with a sheet of filo pastry and brush it with melted butter; keep the remaining filo pastry covered with clingfilm while you work. Repeat with half of the filo pastry sheets, brushing each sheet with butter, and letting them come up the sides of the baking dish. Pour in the cheese filling.
Lay the remaining filo pastry sheets on top of the filling, brushing each with butter. Brush the top of the last sheet with butter; use a sharp knife to score the top sheets into strips about 7cm wide from one end of the baking dish to the other.
Bake in the preheated oven until the pastry is golden brown and crisp, about 45 minutes. Let stand for 5 minutes, then cut into squares and serve hot.
This Greek cheese is available in most of the larger supermarkets and in specialty cheese shops. Pecorino or Parmesan would be a good alternative in this recipe.