In a large mixing bowl, combine the chopped spinach, crumbled feta cheese, onion, garlic, salt, pepper, and nutmeg. Mix until well combined.
Preheat your oven to 375°F (190°C).
Lay out a sheet of phyllo dough on a clean, flat surface. Brush it lightly with olive oil using a pastry brush.
Add another layer of phyllo dough on top and brush it again with olive oil. Repeat this process for a total of 4 layers.
Spoon a line of the spinach and feta mixture along one edge of the layered phyllo dough, leaving about 2 inches of space from the edges.
Gently roll the phyllo over the filling to create a log shape. Tuck in the ends to seal the filling inside. Place the roll seam-side down on a baking sheet lined with parchment paper.
Repeat the process with the remaining phyllo dough and filling until all are used.
Brush the tops of the böreks with the beaten egg for a golden finish.
Bake in the preheated oven for 25-30 minutes, or until the Börek is golden brown.
Remove from the oven and let cool for a few minutes before slicing and serving.