Beat the eggs and sugar until creamy. Stir in the vegetable oil, apple juice, lemon juice and vanilla essence. Mix the baking powder into the flour and add it to the egg mixture, stirring to form a dough. Wrap the dough in cling wrap and refrigerate for 3 hours or overnight.
Prepare the filling: combine the brownie mix, eggs, water and vegetable oil then mix well. Refrigerate the brownie batter for 3 hours or overnight.
Remove the biscuit dough from the refrigerator and let it rest at room temperature for 30 minutes. Mix the egg and tablespoon of water to make an egg wash. Preheat oven to 190 degrees C.
Roll out half the dough on a long piece of baking paper into a rectangle about 1/2 cm thick. Use a large round cookie cutter to cut circles in the dough. Remove the scraps of dough from around the circles.
Using two spoons, place 1 tablespoon of chilled brownie batter in the centre of each biscuit dough circle. Brush the edges of the biscuit circles with egg wash.
Fold the biscuit into a triangular shape, bringing the edges up so they partially overlap the brownie filling. Pinch the corners to seal the dough. Brush the hamentashen with egg wash. Repeat with the remaining circles and the other half of the dough.
Transfer the baking paper holding the biscuits onto a baking tray. Bake in the preheated oven until the bottoms of the biscuits are light golden brown, about 10 minutes.
Try to avoid your temptations to overstuff the hamentashen. Remember, the brownie batter also has a leavening agent in it, so it will rise a bit when exposed to heat and will try to seep out of the hamentashen's sides. For best results, only place 1 tablespoon of batter in the middle of each biscuit.
You may substitute orange juice for the apple juice.