In a sauté pan add the oil, onion and garlic, and cook on medium heat for 3 minutes and add the ground lamb. Break up and brown the lamb, about 4 minutes. Add the tomato sauce and paste, water and spices. Stir to mix through and simmer for 5 minutes.
Chop the olives and drain the chickpeas. Add to the simmering lamb mixture and mix thoroughly. Simmer on low heat for several minutes until thickened. Turn off heat and allow to slightly cool.
Line a rimmed baking sheet with parchment paper. Cut the pastry sheets in half. Lay out the thawed puff pastry sheets, 2 per baking sheet, and make a 1-inch rimmed line on the inside of the edges with a pastry crimper or knife. Don’t go all the way through the dough. Prick the dough with a fork all over in center area.
Bake for 10 minutes, remove from oven and divide the meat mixture evenly over all 4 puff pastry sheets. Top with feta cheese, brush pastry edges with beaten egg (optional) and bake for another 8-10 minutes or until puffed and edges are a golden brown. Top with chopped parsley and serve.