1. Place almonds in a 10-inch baking pan. Bake in a 350° regular or convection oven until golden beneath skins, about 10 minutes. Let cool. In a food processor, pulse almonds with 3/4 teaspoon cinnamon and the granulated sugar until coarsely chopped (or coarsely chop with a knife).
2. Rinse chicken. In a 5- to 6-quart pot, combine chicken, broth, onion, garlic, ginger, turmeric, and cloves. Bring to a boil over medium-high heat; reduce heat, cover, and simmer until chicken is tender when pierced, about 45 minutes.
3. Pour chicken mixture through a strainer set over a large bowl; return strained broth to pan. With your fingers, remove skin from chicken and pull meat from bones; discard skin and bones. Shred chicken into bite-size pieces. Mix chicken and strained onion in a bowl and moisten with about 2 tablespoons broth. Season to taste with salt and pepper. Let cool; if desired, cover and chill up to 1 day.
4. Bring broth in pan to a simmer over medium-high heat; reduce heat to maintain simmer. In a bowl, beat eggs to blend with 1/4 teaspoon salt and 1/8 teaspoon pepper. Add eggs to broth; stir gently until set, 1 to 2 minutes. Pour through a strainer into another bowl; reserve broth for other uses. Let eggs cool.
5. Lightly brush the inside of a shallow 3- to 3 1/2-quart casserole or baking dish with melted butter. Place one 13- by 17-inch sheet of filo in dish so that it covers the bottom and sides of casserole and hangs over the edge slightly. Brush sheet lightly with butter. Repeat to layer and butter three more sheets. Sprinkle half the almond mixture evenly over filo in bottom of casserole; spread chicken mixture over nuts. Cut four sheets of filo in half crosswise to make eight 8 1/2- by 13-inch rectangles. One at a time, brush four half-sheets with butter and layer them over chicken. Sprinkle remaining half of the almond mixture over filo and arrange egg mixture evenly over nuts. Fold in overhanging edges of filo and top with four more buttered half-sheets, tucking any overhanging edges into sides of casserole. Brush top layer with butter.
6. Bake pie in a 375° regular or convection oven until top is well browned, 35 to 40 minutes. Mix powdered sugar with remaining 1/2 teaspoon cinnamon and sift evenly over top of pie. Cut warm pie into portions; serve warm or at room temperature.