Preheat the oven to 350°F (175°C). Lightly grease a 9×13-inch baking dish and set aside.
Dry the Phyllo Dough:
Remove the phyllo dough from its packaging, unroll, and spread the sheets out on a clean surface or baking tray. Allow them to dry at room temperature for 20 minutes. This step is essential to achieve the desired texture in the final cake.
Prepare the Cake Batter:
In a large mixing bowl, combine the vegetable oil, granulated sugar, and eggs. Whisk until well blended. Add the Greek yogurt, orange juice, orange zest, and vanilla extract. Stir until the mixture is smooth. Incorporate the baking powder and salt until just combined. Avoid overmixing.
Assemble the Cake:
Tear or crumble the dried phyllo sheets into small pieces and place them in the prepared baking dish. Pour the cake batter over the phyllo pieces and gently stir to ensure the dough is evenly coated.
Bake:
Transfer the dish to the preheated oven and bake for 35 to 40 minutes, or until the top is golden brown and a toothpick inserted into the center comes out clean.
Prepare the Syrup:
While the cake is baking, combine water, sugar, orange zest, and the cinnamon stick in a medium saucepan. Bring to a boil over medium heat, then reduce to a simmer and cook for an additional 5 minutes. Remove from heat and allow the syrup to cool slightly.
Soak the Cake:
Once the cake is removed from the oven, immediately pour the warm syrup evenly over the hot cake. Let the cake cool to room temperature before transferring it to the refrigerator. Chill for 1 to 2 hours, or until the syrup is fully absorbed.
Serve:
Serve chilled, optionally accompanied by a scoop of vanilla ice cream or a dollop of whipped cream.
Notes
To make this recipe gluten-free:
Replace traditional phyllo dough with a certified gluten-free phyllo alternative (available at specialty stores or online).
Confirm that your baking powder is gluten-free, as some brands may include starches with gluten.
As always, double-check all ingredient labels for hidden gluten-containing additives or thickeners.