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1
Beat the eggs and sugar until creamy. Stir in the vegetable oil, apple juice, lemon juice, and vanilla extract. Mix the baking powder into the flour and add it to the egg mixture, stirring to form a dough. Wrap the dough in plastic and refrigerate for 3 hours or overnight.
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2
Prepare the filling: combine the brownie mix, eggs, water, and vegetable oil and mix well. (You can also follow the package directions and use the low-fat version, if desired). Refrigerate the brownie batter for 3 hours or overnight.
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3
Remove the cookie 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.
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4
Preheat an oven to 375 degrees F (190 degrees C).
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5
Roll out half the dough on a long piece of parchment paper into a rectangle about 1/4 inch thick. Use a large round cookie cutter to cut circles in the dough. Remove the scraps of dough from around the circles.
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6
Using two spoons, place 1 tablespoon of chilled brownie batter in the center of each cookie dough circle. Brush the edges of the cookie circles with egg wash.
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7
Fold the cookie 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.
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8
Transfer the parchment paper holding the cookies onto a baking sheet. Bake in the preheated oven until the bottoms of the cookies are light golden brown, about 10 minutes.
