Cut each piece of Turkish Delight into 6 smaller pieces.
Beat the flour, 1/2 cup sugar, oil, eggs and baking powder in a container until you obtain a homogeneous mixture.
Take a phyllo pastry sheet, smear it with the egg mixture using a brush and cover with a 2nd sheet.
Arrange the pieces of Turkish Delight in the narrow end of the sheet tightly and wrap it into a roll.
Arrange the rolls in a rectangular oiled tray and bake in a preheated 356°F (180 °C) oven until golden.
Prepare the syrup from the remaining sugar, vanilla and 2 cups water - boil until the sugar dissolves completely.
Leave the prepared phyllo pastry to cool and pour on the hot syrup. Leave it for about 4-5 hours to take in the syrup.