Heat oil in heavy large skillet over medium heat. Add onion and sauté until translucent (about 10 minutes). Add cinnamon, ginger, turmeric, and saffron – stir 1 minute. Sprinkle with flour; stir 1 minute. Add broth; bring to simmer. Sprinkle chicken with salt; add to onion mixture. Simmer chicken uncovered until cooked through, making certain to prevent boiling (15 to 20 minutes). Take skillet off heat and add raisins.
When cool enough to handle shred chicken coarsely and return to skillet. Simmer over medium heat until sauce coats chicken thickly. Stir in cilantro and parsley. Season with salt and pepper (to taste). Cool filling completely. Can be made 2 days ahead. Cover; chill.
Combine almonds, powdered sugar, 1/2 teaspoon coarse salt, and cinnamon in mini processor. Pulse until coarsely ground.
Stack 12 phyllo sheets on work surface. Invert 9-inch glass pie dish onto stack. Using dish as a guide; cut phyllo into 10” rounds. Cover phyllo rounds with plastic wrap and damp kitchen towel.
Brush pie dish with melted butter. Place 1 phyllo round on work surface; brush with butter and sprinkle with 1 tablespoon almond mixture. Top with another phyllo round, brush with butter and sprinkle with 1 tablespoon almonds. Repeat with 4 more phyllo rounds, butter, and almonds. Place phyllo stack into prepared pie dish.
Spoon in the filling. Brush each remaining phyllo round with butter and sprinkle with almond mixture. Place stack over filling. Tuck in edges. Brush top of pie with melted butter. Cut 5 slits through the top of pie to allow steam to escape..
Preheat oven to 375°F. Place pie on rimmed baking sheet. Bake uncovered until phyllo is golden and filling is heated through, about 40 minutes. Cool 15 minutes. Invert onto serving plate, sprinkle liberally with powdered sugar and serve.