Cut the chicken into pieces, discarding the skin. Add the butter and oil to a large Dutch oven or other heavy-duty pot and heat on medium until the butter melts.
Add the onion and cook until translucent. Add spices and cook until fragrant.
Add chicken, cover, and cook until very tender.
Transfer cooked chicken, reduce the sauce until most liquids evaporate, and remove cinnamon sticks.
Pick meat off bones, break into pieces, and mix with onion mixture.
Sauté remaining onions, add cilantro, and simmer.
Cook beaten eggs to form a stuffing.
Fry almonds until golden brown, cool, then grind with sugar, orange flower water, and butter.
Oil a round pan, layer with buttered phyllo dough.
Layer chicken filling, egg stuffing, almond mixture, and top with more buttered phyllo dough.
Fold dough edges to enclose the pie and brush with butter.
Top with more phyllo dough layers, tuck edges, and brush with egg yolk and oil.
Bake at 180°C for 30-40 minutes until golden brown.
Coat with powdered sugar and cinnamon before serving.