Heat the olive oil in a large skillet over medium high heat. Add the diced onion and sauté for 3-4 minutes until softened. Add the ground beef and cook, separating any clumps that form until browned and cooked through. Drain any fat over the sink before returning pan to the stove.
Add all the spices and the tomato paste, and stir to combine well. The meat filling is ready, set aside while you assemble your pan.
Mix together the olive oil and melted butter. Lightly brush the bottom of a 9x13 inch pan. Start layering. Add 2-3 sheets of phyllo dough and place on the bottom of the pan. Brush generously with the butter oil mixture, then repeat by adding another 2-3 sheets of phyllo dough on top, and brushing generously with the butter oil. Keep repeating until you are done with about 1/2 the sheets of phyllo dough in the package.
Add the ground beef mixture to the pan and spread evenly. Continue to layer by placing 2-3 sheets on top of the ground beef, brushing generously with the butter/oil mix, repeating with another 2-3 sheets phyllo, and etc. Continue until you've used up all the phyllo sheets.
With a sharp knife, cut the phyllo pie into even squares or diagonals. Cut all the way through to the bottom of the pan, this will make it much easier to lift out slices once baked.
Whisk together the egg and the milk, and add a pinch of salt and pepper to season. Pour this mix evenly over the phyllo pie.
Bake in the middle rack of the oven for about 45 minutes or until golden brown and crispy. Serve warm, preferably with a side salad or yogurt. Enjoy!
For tips on how to work with phyllo dough, check the post above.