Make the filling by combining the ground walnuts with the beaten egg and sugar.
Fold each phyllo pastry sheet into 3 lengthwise, smear with the melted butter. Put 1 tbsp of the filling at the end, fold the sheet into a triangle.
Place the triangles in a buttered oven dish. Smear them with butter on top and bake at 356°F (180 °C) to a nice crisp.
Pour the hot syrup over the cold baklava, cover with a towel and let it sit for at least 12 hours.