Bring first 13 ingredients to a boil in a Dutch oven; reduce heat, cover, and simmer, stirring occasionally, 45 minutes or until chicken is tender. Remove chicken, and set aside.
Stir eggs into simmering broth; cook, stirring constantly, 2 to 3 minutes. Pour into a colander; drain 30 minutes. Place solids in a bowl.
Skin and bone chicken; cut into bite-size pieces, and stir into egg mixture.
Unfold phyllo, and cover with a damp towel to prevent drying.
Brush a 10-inch cast-iron skillet with melted butter. Stack 4 phyllo sheets in skillet in a crisscross pattern, brushing each with butter and allowing edges to overhang. Crumple 2 phyllo sheets, and place in center of skillet.
Stir together powdered sugar, 1 tablespoon cinnamon, and 1 1/2 teaspoons sugar; sprinkle one-third mixture over phyllo, and sprinkle with 1/2 cup almonds. Stack 2 phyllo sheets over almonds, brushing each with butter. Spoon half of chicken mixture over phyllo. Crumple 1 phyllo sheet, and place in skillet. Stack 2 phyllo sheets over crumpled phyllo, brushing each with butter. Sprinkle with half of remaining powdered sugar mixture, and remaining 1/2 cup almonds. Stack 2 phyllo sheets over almonds, brushing each with butter. Crumple 1 phyllo sheet, and place in skillet. Spoon remaining half of chicken mixture over phyllo. Stack 2 phyllo sheets over chicken mixture, brushing each with butter. Fold draping edges over stack. Drizzle with remaining melted butter.
Bake at 400° for 20 minutes or until golden. Invert onto a serving platter, and sprinkle with remaining powdered sugar mixture.