For the dough:
1 cup all-purpose flour, plus more for dusting
3/4 cup whole-wheat flour
1 teaspoon baking powder
1/4 teaspoon fine salt
10 tablespoons (1 1/4 sticks) unsalted butter, at room temperature
2/3 cup packed light brown sugar
1 large egg
1 teaspoon vanilla extract
1 medium orange
For the filling:
8 ounces dried apricots
1/4 cup water
1 tablespoon honey
For the dough: Whisk the flours, baking powder, and salt together in a medium bowl.
Beat the butter and brown sugar in the bowl of a stand mixer fitted with the paddle attachment on medium speed until light and fluffy, about 3 minutes. Stop the mixer and add the egg and vanilla. Using a Microplane, finely grate the zest of the orange into the bowl (save the zested orange for the filling). Beat on medium speed until incorporated. Stop the mixer and scrape down the sides of the bowl and the paddle with a rubber spatula.
Return the mixer to low speed, gradually add the flour, and mix until just combined (the dough will be very soft and sticky). Scrape the dough onto a sheet of plastic wrap and press into a disk about 1-inch thick. Wrap the disk tightly in the plastic wrap and refrigerate until firm, but still pliable, about 2 hours. Meanwhile, make the filling.
For the filling: Place the apricots in the bowl of a food processor fitted with the blade attachment and process until finely chopped, about 30 seconds. Transfer the mixture to a small saucepan. (No need to wash out the food processor; you will use it again.)
Juice the zested orange and add 2 tablespoons of the juice to the pan. Add the water and honey. Heat the mixture over medium heat, stirring occasionally, until the apricots plump up and all the liquid is absorbed, about 4 minutes.
Transfer the mixture back to the food processor and process into a smooth paste, about 1 minute. Let the mixture cool completely.
To assemble: Line a baking sheet with parchment paper and set aside. Transfer the cooled apricot mixture to a piping bag or resealable plastic bag.
Dust a work surface generously with flour. Unwrap the disk of dough and cut it into 3 equal pieces (about 6 1/2 ounces each). Place one piece on the work surface, rewrap the other 2 pieces back in plastic wrap, and refrigerate those 2 pieces.
Reshape the remaining piece of dough into a log about 2 inches wide and 4 inches long. Place the log with the short side facing you, generously dust the top with flour, and roll into a 1/2-inch-thick rectangle about 4 inches wide and 12 inches long.
Using kitchen shears, snip off a bottom corner of the plastic bag or piping bag. Pipe enough filling