Wash the squabs and place in a pan with the butter, onion, cinnamon stick, ginger, cilantro, parsley and turmeric. Season with salt and pepper. Add just enough water to cover and bring to a boil. Cover and simmer gently for about 1 hour, until the squab is very tender.
Strain off the stock and reserve. Skin and bone the squabs, and shred the flesh into bite-sized pieces. Preheat the oven to 350°F Combine the sugar, cinnamon and almonds, and set aside.
Measure ⅔ cup of the reserved stock into a small pan. Add the eggs and mix well. Stir over low heat until creamy and very thick and almost set. Season with salt and pepper.
Brush a 12-inch diameter ovenproof dish with some of the melted butter and lay the first sheet of pastry in the dish. Brush this with butter and continue with five more sheets of pastry. Cover with the almond mixture, then half the egg mixture. Moisten with a little stock.
Layer four more sheets of phyllo pastry, brushing with butter as before. Lay the squab meat on top. Add the remaining egg mixture and more stock. Cover with the remaining pastry, brushing each sheet with butter, and tuck in overlapping edges.
Brush the pie with egg yolk and bake for 40 minutes. Raise the oven temperature to 400°F and bake for 15 minutes more, until the pastry is crisp and golden. Garnish with a lattice design of cinnamon and confectioners’ sugar. Serve hot.