Preheat oven to 350 degrees F and grease a 9×13-inch baking dish. Set aside.
Open packages of phyllo dough and unroll. Spread sheets out on a baking sheet or clean surface and allow them to dry out for 20 minutes.
As phyllo is drying out, prepare the cake batter. In a large bowl, combine the oil, sugar, and eggs and whisk to combine.
Mix in yogurt, orange juice, orange zest, and vanilla until smooth, then mix the salt and baking powder until just combined. Don’t overmix.
Tear or crumble the dried phyllo dough into small pieces and place in the prepared baking dish. Use both rolls of phyllo dough, it will compress.
Pour the batter over the phyllo dough and gently mix to combine.
Bake for 35-40 minutes or until golden on top and an inserted toothpick comes out clean.
As the cake bakes, prepare the syrup. In a small saucepan, combine the water, sugar, orange, zest, and cinnamon stick and cook over medium heat to bring the mixture to a boil. Reduce heat to a simmer and cook for 5 more minutes or until it begins to thicken. Allow syrup to cool.
Remove cake from oven and pour the syrup over the top while still hot.
Allow the cake to come close to room temperature, then place in the fridge until the syrup has fully absorbed, about 1-2 hours.
