¾ cup all-purpose flour
½ cup whole wheat flour
½ teaspoon baking powder
¼ teaspoon salt + Pinch of salt, divided
6 tablespoons unsalted butter, softened
¾ cup light brown sugar
1 egg, at room temperature
2 teaspoons vanilla extract
8 ounces dried Turkish or Calimyrna figs, stemmed and quartered
2 cups apple juice
2 teaspoons lemon juice
1. Preheat oven to 350 degrees F. Line an 8-inch square baking pan with aluminum foil, allowing excess to hang over the pan edges. Grease the foil; set pan aside.
2. Combine the flours, baking powder, and ¼ teaspoon of salt in a small bowl. With an electric mixer on medium-high speed, beat the butter and sugar until light and fluffy, about 2 minutes. Beat in the egg and vanilla until combined. Stir in the flour mixture until just incorporated. Place all but ¾ cup dough into the prepared pan and spread into an even layer. Bake until just golden, about 20 minutes. After you put the bottom crust in the oven, roll the remaining dough into an 8-inch square between two sheets of greased parchment paper, then place in the freezer until firm, about 30 minutes.
3. Meanwhile, cook the figs, apple juice, and the remaining pinch of salt in a saucepan over medium heat, stirring occasionally, until very soft and syrupy, 15 to 20 minutes; cool slightly. Process the mixture with the lemon juice in a food processor until jam-like.
4. Spread the fig mixture evenly over the baked crust. Top with the frozen dough square and press lightly on the dough to adhere. Bake until the top is golden brown, 25 to 30 minutes. Cool completely on a wire rack, about 2 hours. Using the foil overhang, lift bars from pan and cut into squares. Store leftovers in an airtight container at room temperature.