Pulse the flour, granulated sugar, baking powder and salt in a food processor. Add the butter; pulse until the mixture looks like coarse meal. Add 2 eggs; pulse until the dough forms a ball. Transfer to a floured surface; knead just until smooth. Shape into a 5-by-12-inch rectangle on a piece of plastic wrap; wrap and chill 1 hour.
Pulse the pistachios in the food processor until finely chopped; transfer to a bowl. Pulse the apricots until finely chopped. Return the pistachios to the food processor along with the honey, orange zest and juice, and almond extract; pulse to combine. Refrigerate.
Position racks in the upper and lower thirds of the oven; preheat to 375 degrees F. Line 2 baking sheets with parchment. On a floured surface, cut the dough lengthwise into four 1 1/4-inch-wide strips. Roll 1 strip into a 3-by-18-inch rectangle. Spoon 1/3 cup of the pistachio mixture down the length. Starting from a long side, roll into a log to enclose the filling. Pinch the seam to seal; arrange seam-side down. Cut into 2-inch pieces and put on a baking sheet; refrigerate. Repeat with the remaining dough and filling.
Make 1/2-inch-long cuts on the cut ends of each piece of dough; pull apart to form an X. Arrange 1 inch apart on the baking sheets. Beat the remaining egg and brush on the cookies. Bake, switching the pans halfway through, until the cookies are light golden, about 15 minutes. Let cool 5 minutes; transfer to racks to cool completely. Dust with confectioners' sugar.
Photograph by Levi Brown
Recipe courtesy of Food Network Magazine