Soak the apricots. Place the apricots in a medium bowl. Add boiling water to cover and set aside to soak for 1 hour.

Make the filling. Drain the apricots in a colander, stirring to eliminate the surface water, and then blot dry on paper towels. Transfer them to a chopping board or bowl and finely chop. Mix the apricots, walnuts if using, and the remaining 1/2 cup sugar in a medium bowl, stirring until well combined.

Mix the dough. Whisk together the flour and baking powder in a medium bowl. Whisk together the eggs, oil, 1 cup of the sugar, and the lemon zest and orange zest in a large bowl, whisking until the sugar is dissolved and the mixture is creamy and foamy. Sift the flour mixture into the egg mixture, stirring together with a wooden spoon until combined and a dough forms. Wrap the dough in plastic wrap and refrigerate for 1 hour.

Make the cookies. Preheat the oven to 350°F. Spray two baking sheets with nonstick cooking spray. Roll out the dough on a lightly floured board to 1/4-inch thickness. Cut out 3-inch circles (use a biscuit cutter). Place a generous spoonful of filling in the center of each circle, then fold up three sides so the cookie looks like a 3-cornered hat, pinching the dough edges together but leaving the center open.Gather the dough scraps and reroll; cut and fill in the same way.

Arrange the cookies on the prepared baking sheets and lightly brush with the egg wash, which will give them a nice color.

Bake until the pastry is golden brown—20 to 25 minutes. Transfer the cookies from the baking sheets to wire racks to cool.