Prepare the filo. Cut the filo into thick strips. Toss and separate them. Spread them fluffily onto a large sheet pan. Leave them to air-dry for at least an hour at room temperature.
Make The Syrup. Add all of the ingredients for the syrup (honey, sugar, water, lemon juice, and zest) to a saucepan and bring to a boil. Cook for 5-6 minutes until slightly thickened. Set aside.
Preheat oven to 170°C / 340°F.
Prepare the cake batter. Add the yogurt, vanilla extract, sugar, baking powder, and baking soda to a large mixing bowl and whisk to combine.
Whisk in the eggs and then the oil.
Add the filo in batches, stir with a pastry spatula, and break the filo apart as you stir so it won't lump.
Grease a round 10-inch (26 cm) pan (not a springform pan) with oil.
Transfer the filo cake batter to the pan and smooth the surface with a spoon.
Bake for 35-40 minutes until the top is honey-brown and a toothpick inserted in the center of the cake comes out clean. Note: the toothpick might look moist, but shouldn't have fragments on it.
Ladle the syrup over the hot cake. Poke the cake with a toothpick to help it. The syrup might look like it's a lot, but it will be absorbed. Let the cake stand at room temperature for a couple of hours to absorb the syrup.
Refrigerate the cake for at least 3-4 hours prior to serving.
Cut into 12 pieces and serve with a scoop of Greek Yogurt or Whipped Cream on top. Fresh strawberries are also amazing with this cake.