Preheat oven to 350 degrees f. and line two baking sheets with parchment paper.
Mix together the wet ingredients: egg, oil, sugar and vanilla extract. Add the dry ingredients: flour, baking powder and salt, and stir until a smooth dough is formed.
Roll out the dough to around ¼ inch thick. Cut circles using a cookie cutter or a glass cup.
Place 1 teaspoon of the filling in the center of the circles and pinch closed to form a triangle.
Bake the hamantaschen for 10-12 minutes. Transfer to a wire rack to cool.