Combine 2 cups sugar, water, and cinnamon in a saucepan over medium-high heat. Squeeze in orange juice and add juiced halves. Bring to a boil and boil vigorously for 8 minutes. Remove from heat and allow to cool while you prepare the cake.

Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 9x13-inch baking pan.

Remove phyllo sheets from the package. Tear or slice sheets roughly into shreds and pile up in the baking pan. Let shredded phyllo dry out a little while you prepare the remaining ingredients.

Cut 1 orange in half, and slice 1 half into very thin half-moons to garnish the cake. Zest and juice the remaining 2 1/2 oranges.

Combine orange juice, orange zest, eggs, yogurt, olive oil, 1/2 cup sugar, and baking powder in a blender or food processor. Pulse several times in short bursts just until the mixture is smooth and all ingredients are well blended. Pour the mixture over the shredded phyllo in the baking pan. Stir everything together gently to ensure that the wet mixture is evenly distributed and no dry phyllo shreds remain. Garnish top of the cake with the orange slices.

Bake in the preheated oven until the top is golden and the filling is set, about 45 minutes. A toothpick inserted in the center should come out clean. Remove from the oven and immediately ladle the cooled syrup over the hot cake.

Set cake aside for at least 1 hour or overnight, until most of the syrup has soaked in. Slice into squares and serve.