In a large skillet, heat 2 tablespoons of olive oil over medium heat. Add the chopped onion and garlic, sautéing until the onion becomes translucent.
Add the ground beef or lamb to the skillet. Cook until browned, breaking it up with a spoon. Drain any excess fat.
Stir in the chopped parsley, cumin, salt, and black pepper. Cook for an additional 2-3 minutes, then remove from heat and let it cool.
Preheat your oven to 180°C (350°F). On a clean surface, lay out one sheet of phyllo dough and brush it lightly with olive oil. Place a spoonful of the meat mixture at one end and fold the sides over to enclose the filling. Roll it up tightly into a cylinder shape.
Repeat the process with the remaining phyllo dough and filling. Place the rolled bourak on a baking sheet lined with parchment paper. Brush the tops with the beaten egg.
Bake in the preheated oven for 25-30 minutes, or until golden brown and crisp. Serve hot.