Put the prunes and apricots into a large pot filled with water and bring to a rolling boil over high heat. Cook the fruit uncovered, stirring occasionally, until tender, about 15 minutes. Drain the fruit in a colander and mash together in a bowl using a fork. Set aside.

Preheat the oven to 350 degrees F (175 degrees C).

In a bowl, whisk together the eggs, 1 cup sugar, safflower oil, lemon zest, and orange zest. In a separate large bowl, sift together the flour and baking powder. Stir in the egg mixture and knead with your hands until the dough forms. Roll out the dough on a lightly floured surface to about 1/4 inch thickness. Use a cookie cutter or the rim of a drinking glass to cut out circles.

Combine the mashed prune and apricot mixture with lemon juice, chopped walnuts, and 1/3 cup sugar in a bowl. Place a tablespoon of this filling in the center of each dough circle. Pinch the edges firmly together to form a triangle, leaving the center open to show the filling. Repeat with the remaining dough and filling.

Bake the hamantaschen in the preheated oven until they turn golden brown, about 20 minutes. Let them cool in the pans for 10 minutes before transferring to a wire rack to cool completely.