Preheat the oven to 350 F.
Place the feta in a bowl and mash with a fork.
Add the Gruyere, egg and pepper and mix.
Cut the filo sheets in halves width ways. Keep the unused pastry covered and prevent from drying.
Place one half of one sheet lengthways. Brush with the combined oil and butter, and then fold into thirds lengthwise.
Brush with the oil and butter. Place 1 tablespoon of the cheese mixture on corner of the pastry strip. Fold corner over the filling to the edge of the pastry to form a triangle.
Continue to fold until the filling is enclosed and the end of the pastry is reached.
Place the triangles on a lightly greased baking tray and brush them with the oil and butter mixture.
Bake for 20 minutes, or until crisp.