Place an oven rack in the center of the oven and preheat to 350 degrees F.
Butter the bottom and sides of a 9-by-13-inch glass or ceramic baking dish. Line the bottom with an 8-by-20-inch piece of parchment paper, allowing the excess paper to hang over the sides.
For the crust: Whisk the all-purpose flour, almond flour, baking powder, salt and baking soda in a medium bowl.
Beat the sugar and butter using an electric hand mixer until combined in a large bowl. Beat in the egg, cream and vanilla until smooth. Add the dry ingredients and beat until the mixture forms into clumps. Press the clumps together to form a dough. Knead the dough for 30 seconds and wrap in plastic. Refrigerate for 1 hour.
For the filling: Place 1/4 cup water, the figs, orange juice, vanilla extract and orange zest in a food processor. Blend until the figs are finely ground, about 2 minutes. Add the almond butter and blend until incorporated. Add the almonds and pulse until combined.
Remove the plastic from the dough and cut in half. Roll out 1 piece of dough into an 8-by-12-inch rectangle on a well-floured work surface. Cut the dough in half lengthwise and then in half crosswise to make 4 equal-size pieces of dough. Transfer the dough pieces to the prepared baking dish using a spatula, and arrange in a single layer. Pinch the edges of the dough together to seal. Spoon the filling onto the dough. Spread the filling evenly over the dough using damp hands. Smooth the top of the filling using a rubber spatula. Roll out the remaining dough into an 8-by-12-inch rectangle. Cut into 4 equal pieces and place on top of the filling, pinching the edges of the dough together to seal. Bake until golden, 25 to 30 minutes. Place the baking dish on a wire rack to cool completely, about 1 hour.
Using the excess parchment paper as handles, remove and place on a cutting board. Cut the cookie into twenty-four 1 1/2-inch-square pieces and serve.
To toast the almonds, arrange in a single layer on a baking sheet. Preheat the oven to 350 degrees F. Bake until lightly toasted, 6 to 8 minutes. Cool completely before using.