In a large skillet, heat a drizzle of olive oil over medium heat. Add chopped onion and garlic, sauté until the onion is translucent, about 5 minutes.
Add the chopped spinach to the skillet and cook until wilted, about 3 minutes. Remove from heat and let it cool slightly.
In a mixing bowl, combine the shredded chicken, ricotta, feta, sautéed spinach with onion and garlic, nutmeg, salt, and pepper. Mix until well combined.
Lay out one sheet of filo pastry on a clean dry surface and brush it lightly with melted butter. Place another sheet on top, repeating the process to make 5 layers.
Spoon the chicken and spinach mixture along one edge of the layered filo, shaping it into a log. Fold the sides of the filo over the filling and roll it up tightly into a cylinder. Repeat this process with the remaining filo and filling.
Place the rolled filo pies seam-side down on a lined baking tray. Brush the tops with beaten egg 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 allow to cool for a few minutes before slicing.
Notes
Allow the pie to cool slightly before slicing for easier serving.