We start by shredding the phyllo sheets into small pieces into a baking pan. Mix them to become airy and leave them for 15-20 minutes to dry. Mix regularly.
In the meantime we put in the mixer's the margarine, sugar and beat, until the sugar has dissolved. Add the yogurt, vanilla extract, orange zest, baking powder, eggs, one by one and continue beating to combine.
Brush a medium sized baking pan with margarine, dust with flour and shake to remove excess. Spread 1/3 of the phyllo pieces and pour over 1/3 of the batter. Continue doing so with the remaining phyllo and batter.
Bake in the preheated oven for about 40-45 minutes.
In the meantime we prepare the garnishment: Sprinkle the orange slices and peel strips with sugar. Melt the margarine in a non stick frying pan and then add orange slices and strips. Pour over the cognac and saute, until caramelized. Remove frying pan from heat and set aside the caramelized oranges.
Remove the pan from the oven and let the "portokalopita" cool off.
To prepare the syrup: Put in a medium saucepan all the ingredients for the syrup and boil for about 7-8 minutes, until thickened. Remove saucepan from the heat and remove orange peel. Allow syrup to cool for about 6-7 minutes.
Prick the cake's surface with a small knife, pour over the syrup and allow absorption. Garnish the "portokalopita" with the caramelized orange slices and strips and then serve.