Make the dough: In the bowl of an electric mixer fitted with the paddle attachment, beat the butter and sugar until light and fluffy, about 2 minutes. Beat in the egg, then the vanilla, then the orange zest, beating well after each addition.
In a separate bowl, combine the all-purpose flour, whole wheat flour, baking soda, and salt. Add the dry ingredients to the wet and mix on low speed, just until combined.
Cover the dough with plastic wrap and refrigerate for at least 2 hours or for up to 2 days.
Meanwhile, make the filling: In a medium saucepan, combine the figs, orange juice, orange zest, and salt. Add ½ cup water and bring to a simmer over medium heat. Reduce the heat to low and simmer until the liquid is mostly evaporated and the figs are softened, about 10 minutes.
Transfer the fig mixture to a food processor along with the maple syrup. Process into a smooth paste, scraping down the sides of the bowl with a rubber spatula as needed. Transfer the paste to a gallon-sized zip-top bag.
Preheat the oven to 350°F. Grease a large baking sheet with cooking spray or line with parchment paper or a silicone baking mat.
On a lightly floured work surface, roll the dough into a 12x12-inch square that is about ¼ -inch thick. If the dough is too cold to work with, let it sit at room temperature for 2 to 3 minutes. With pizza cutter, slice the dough into four equal strips 3 inches wide.
Snip off a corner of the bag with the filling. Pipe a line of filling (about 1 inch thick) down the center of each strip of dough. Gently fold the dough over the filling to shape into a flattened log—fold each of the 2 long sides over the filling in turn so that the final log is in thirds as if you were folding a letter for an envelope. Gently flip and press on the log to seal the edges closed. Cut the logs into 2-inch pieces.
Place cookies seam-side down on the prepared baking sheet. Bake for 17 to 18 minutes, until set and firm. Remove from the oven and immediately stack the warm cookies in an airtight container with a paper towel between each layer. Seal closed for at least 6 hours before serving (this yields a softer texture).
Notes
Adapted from Serious Eats, who had the great tip about storing the bars while still warm.
TO STORE: Store these fig bars in an airtight container for up to 5 days or in the refrigerator for up to 10 days. Bring to room temperature before serving.
TO FREEZE: Freeze the cooled fig bars in a freezer bag or airtight container for up to 2 months. Thaw overnight in the refrigerator or at room temperature.