Preheat the oven to 180°C (360°F).
Remove about a tablespoon of orange peels from the syrup and chop them finely. Leave the remaining peels in the syrup.
Using an electric mixer, whisk the eggs and sugar until they become white and fluffy.
Add the chopped orange peels, Greek yogurt, vanilla extract, baking powder, and a pinch of salt. Mix until well combined.
Add the vegetable oil and mix again until combined.
In a small bowl, mix 50 ml (1.7 fl.oz) of orange juice with 1 tsp of baking soda. As soon as it starts to bubble, pour it into the batter and mix until combined.
Finally, crush the dried phyllo into small pieces and add it to the batter a little at a time until all the phyllo dough is covered.
Grease a 25x25 cm pan with vegetable oil and pour the batter into it, flattening it slightly to make it even.
Bake for 40-45 minutes at 180°C (360°F) until golden.
Once the cake is out of the oven, use a skewer to poke some holes in the middle. Then, pour the cold syrup over it right away. Allow the Portokalopita – Greek orange pie to absorb the syrup for at least an hour before serving.