Preheat oven to 150°C / 302°F.
Cut all of the phyllo into 2,5 cm / 1-inch pieces.
Add in a 26 x 36 / 11 x 15-inch pan. Try to separate most pieces from each other.
Place pan in the oven and cook the phyllo for 45 minutes. Every 15 minutes toss and flip the phyllo pieces so they will dry evenly. This is done in order to dry the phyllo. Once it has dried and gotten really crispy and flaky remove it from the oven.
Raise the oven's temperature to 170°C / 338°F.
In a mixing bowl add the eggs, and sugar, and blend with a hand whisk until lightly foamy. Whisk in the yogurt and then add the corn oil. Mix in the orange zest, vanilla extract, and baking soda as well.
Stir in handfuls of the phyllo at a time while stirring well with a spoon. Once all of the phyllo is incorporated, grease the same pan you used for the phyllo with some oil.
Spread the batter in the pan. Bake for 30-35 minutes until it gets a nice golden brownish color on top. Prick with a knife to see if it comes out clean.
Pour the cool syrup over the hot pie using a ladle, and by adding spoonfuls at a time.
Let the pie reach room temperature before refrigerating. You can serve it both at room temperature or cool from the fridge.
You may also serve the orange pie with a spoonful of Greek yogurt and some ground cinnamon on top.