Lay out the phyllo sheets individually on a surface and let them dry thoroughly for about 2 hours. Once dry, crumble them into coarse pieces and transfer them to a large bowl. Set aside.
Preheat oven to 160°C/ 320°F, at convection mode.
Prepare the oranges: Poke the surface of 2 oranges with a fork. Place them in a saucepan with water and simmer over medium heat until very soft. Once tender, remove them from the heat and let them cool.Note: You will use a total of 4 oranges for this recipe — 2 for puréeing and 2 for juicing later. Once the oranges are cool, squeeze out as much juice as possible and set it aside. Then, blend the oranges into a smooth purée using a food processor.
In a large bowl, whisk together the eggs and granulated sugar until the mixture is light and pale. Add the strained yogurt, sunflower oil, baking soda, baking powder, vanilla extract, orange blossom water, and the orange purée. Mix well.
Squeeze the juice from the remaining 2 oranges and add it to the bowl, stirring to combine.
Toast the slivered almonds in a small pan over medium to high heat until golden brown. Once toasted, add them to the bowl with the rest of the mixture.
Gradually fold in the crumbled phyllo dough using a spatula, ensuring everything is well combined. The mixture should be thick but evenly moistened.
Grease and flour a rectangular baking pan (approximately 34x25cm / 13x10in). Pour the mixture into the pan and spread it evenly.
Bake in the preheated oven for 40-45 minutes, or until the top is golden brown and crispy. Remove from the oven and let it cool.