Preheat the oven to 180°C (350°F).

In a large skillet, heat the olive oil over medium heat. Add the sliced leeks and sauté until they are soft and translucent, about 5-7 minutes. Remove from heat and let cool slightly.

In a mixing bowl, combine the sautéed leeks, crumbled feta cheese, grated mozzarella cheese, ricotta cheese, salt, black pepper, and nutmeg (if using). Mix well until all ingredients are thoroughly combined.

Lay out a sheet of phyllo pastry on a clean surface. Brush lightly with melted butter. Place another sheet on top and brush with butter again. Repeat this process with 3-4 sheets.

Place a generous amount of the leek and cheese filling along one edge of the layered phyllo, leaving some space at the sides.

Fold the sides over the filling, then carefully roll the phyllo to enclose the filling, forming a log shape. Place the rolled börek seam side down on a baking sheet lined with parchment paper.

Beat the egg in a small bowl and brush the top of the börek with the egg wash for a golden finish.

Bake in the preheated oven for 25-30 minutes, or until the pastry is golden brown and crispy.

Remove from the oven and let it cool for a few minutes before slicing into pieces. Serve warm.