Thaw the phyllo pastry overnight in the refrigerator, then let it rest at room temperature before using. This keeps it flexible and prevents tearing while layering.
Heat olive oil in a pan and brown the ground meat, breaking it apart as it cooks. Add onions, leeks, and spices, then cook until soft and fragrant. Remove from heat and stir in parsley.
In a bowl, whisk milk, Greek yogurt, water, olive oil, eggs, salt, and pepper. This mixture helps keep the phyllo moist inside while baking crisp on top.
Grease the baking pan and layer two sheets of phyllo at a time, drizzling batter between layers. Use half the phyllo, spread the meat filling evenly, then finish with the remaining phyllo layers.
Slice the pie into portions before baking, pour remaining batter on top, and bake until golden and crispy. Let it rest briefly before serving so it sets nicely.