Put sugar, orange juice, cinnamon, and water in a saucepan and bring to a boil. Reduce the heat and let it simmer for 5 minutes (you can add the leftover orange peel if desired). Cook over low heat for another 10 minutes. Let cool completely.
For the Cake
Fold fillo sheets like a harmonica and leave them to dry, and then tear or crunch into small pieces.
Preheat the oven to 350 degrees Fahrenheit and grease a 12-inch cast-iron skillet lightly with oil.
Using an electric mixer, beat the eggs and sugar, and then add yogurt, oil, and baking powder. Mix in the orange zest and vanilla to the mixture. Gradually add the chopped fillo (by handfuls), gently mixing with a spatula or wooden spoon to incorporate.
Pour the mixture into the prepared skillet and bake for 40-45 minutes, or until golden brown.
Take out the cake, prick it with a fork, and immediately pour the cooled syrup over the hot cake. Set aside for at least 2 hours, until most of the syrup has soaked in. Refrigerate until serving.
Fillo (phyllo or filo): Defrost the fillo beforehand! Make sure to dry it before adding it to the batter thoroughly. This will ensure that the mixture is evenly distributed and not create dough blobs resulting in doughy clumps later on. You can also tear the pastry sheets first and then spread them out and leave them to dry. To speed up the process of drying, place a baking sheet with fillo into a warm oven.
Syrup: Always pour cold syrup over hot cake. You could also let the cake cool first and then pour it over with hot syrup, but that adds extra cooling time. Also, try to keep some syrup in a bottle or bowl for later. This way, you can drizzle some as you serve the portions.
Orange Zest: Mix the zest with baking powder to prevent it from clumping.
Serving: If you wish, top the cake with thinly sliced oranges before baking to add a visual appeal. Drizzle the slices with chocolate syrup before serving. Another way to enjoy this delightful cake is to add a scoop of ice cream or yogurt on top when you serve it, especially on a hot summer day.
Make-Ahead: This Greek orange fillo cake is perfect for making ahead of time! It needs to cool completely for at least 2 hours for the syrup to settle into the cake base fully, so it can easily be made the day before you plan to serve it.
Storing: The baked cake, including leftovers, should be stored, lightly covered, in the refrigerator for up to 4 days.
Skillet: If you don't own a cast-iron skillet yet, I highly recommend getting one. You can find them at a pretty affordable price. However, you can make this cake in a 9x13 baking dish or two 9-inch round cake pans.
Please keep in mind that nutritional information is a rough estimate and can vary significantly based on its products.