Make the syrup first
The syrup must be completely cold when it goes on the warm cake, so make it well ahead. Combine the sugar, water, orange peel strips and cinnamon stick in a small saucepan. Bring to a boil over medium heat, stirring until the sugar dissolves. Add the orange juice and simmer for 5 to 7 minutes until the syrup has thickened slightly and is glossy. It should coat the back of a spoon lightly. Remove from heat. Discard the orange peel strips and cinnamon stick. Allow to cool completely to room temperature, then refrigerate until needed.
Make the batter
Preheat your oven to 340°F / 170°C. Grease a rectangular or square baking pan generously with olive oil. A 30cm x 20cm (12 x 8 inch) pan or a 25cm x 25cm (10 x 10 inch) square pan both work.
In a large bowl, beat the eggs and sugar together with a whisk or electric mixer until pale and slightly thickened, approximately 3 to 4 minutes. Add the olive oil and whisk until fully incorporated. Add the Greek yogurt, orange zest, orange juice, vanilla extract and cinnamon. Whisk until completely smooth and unified. Add the baking powder and whisk through.
Add the phyllo
Add the dried, crumbled phyllo to the batter in two or three additions, folding gently after each addition to coat the phyllo pieces in the batter without crushing them completely. The mixture should look rough and irregular, with visible pieces of phyllo throughout a smooth batter base. This is correct. Do not overmix. You want the phyllo pieces to retain some of their individual character.