First, get the filo ready. Preheat the oven to 100 C and lightly scrunch each filo sheet into a roll and place it in on an un-greased baking tray. If needed, do this step in batches. See photos below.
Bake the filo for 20 to 30 minutes, turning each sheet over halfway through, until they feel very dry and crispy to the touch. When you can comfortably handle them, crush each sheet into small pieces, as fine as possible. Set aside to cool.
Next, make the syrup. Combine the syrup ingredients in a small saucepan on high heat and bring to a boil. Then simmer it on low for 15 to 20 minutes till the sugar has completely dissolved. Set aside to cool completely. It will be poured over the hot cake once it's baked.
Now, make the cake batter. Preheat the oven to 175 C and grease an 8-inch springform pan (or a regular round cake pan).
In a mixing bowl, combine the sugar and orange zest and rub the two together with your fingertips to release more flavour. Add the eggs and whisk vigorously (or use a hand mixer) till pale and frothy, 1 to 2 minutes.
Add the yoghurt, vanilla, baking powder and baking soda. Whisk to combine, followed by the olive oil and orange juice, whisking again.
Gradually add the crushed filo, folding it into the batter with a spatula as you go. Adding it all at once could cause the filo to clump together.
Once it's all incorporated, spread the batter into the prepared pan and bake for 25 to 30 minutes until golden-brown on the top and a toothpick poked in the center comes out clean.
As soon as the cake is out, use a skewer or fork to poke holes all over the surface, going about halfway in. Pour the syrup, one spoon at a time, waiting till it's absorbed before adding more (this happens quite quickly). If needed, carefully tilt the pan from side to side to distribute any syrup that may have pooled around the edges.
Let the cake cool completely at room temperature. Slice and serve with a little cream! It actually tastes even better the next day, so if possible, refrigerate it overnight. Store in the fridge in an airtight tin for 4 to 5 days. Happy baking!