In a large skillet, heat the vegetable oil over medium heat. Add minced garlic and stir for about 1 minute until fragrant.

Introduce the ground beef and cook until browned, about 5-7 minutes. Season with salt, black pepper, and ground cumin. Stir in tomato paste and cook for 2-3 more minutes. Set aside to cool.

Preheat oven to 375°F (190°C). Mix melted butter with olive oil in a small bowl. Brush a casserole pan with the mixture, layer half of the phyllo sheets brushing each with the butter mixture as you go.

Spread the cooled beef filling evenly over the phyllo.

Layer the remaining phyllo sheets, brushing each with the butter-olive oil mixture. Whisk together milk, egg, a pinch of salt, and black pepper in a separate bowl. Pour this over the assembled layers.

Transfer the pie to the preheated oven and bake for about 50 minutes or until the top is golden brown and crispy. Keep an eye on it to prevent over-browning.

Let the pie cool for about 10 minutes before slicing and serving warm, ideally with a fresh salad or yogurt.