Make the dough: In a large bowl, stir together flours, cinnamon, nutmeg, baking soda, and kosher salt until well combined. In a medium bowl, whisk together sugar, honey, ginger, orange zest, egg, butter, and oil until smooth. Pour wet ingredients into flour mixture and fold until a cohesive dough forms.

Halve dough and place each half between two pieces of parchment paper. Using a rolling pin, roll each dough into a 15”-x-5” rectangle, about ⅛”-thick. Leave dough between parchment, layer on a baking sheet and refrigerate, 1 hour.

Meanwhile, make the filling: In a medium pot over medium heat, combine figs, dates, orange juice, water, butter, and rum (if using). Bring to a boil and cook, stirring occasionally, until liquid is syrupy and mostly absorbed, 4 to 5 minutes. Let cool completely.

Transfer fig mixture to a food processor, add vanilla and zests, then process until smooth.

Working with one sheet of dough at a time, peel off top layer of parchment. Using an offset spatula or spoon, spread half the fig filling in a 2”-wide strip down the length of the dough. Use bottom layer of parchment to help bring naked edges of dough to meet over and enclose the filling, pressing down the seam to seal. Gently press cookies into a 2”-wide bar.

Repeat with remaining dough and filling. Transfer both bars to the freezer until firm, at least 15 minutes and up to overnight.

Preheat oven to 350°. Line a baking sheet with parchment paper.

Remove cookie bars from the freezer. Using a sharp knife, cut each bar into ten 1½” pieces and place on prepared sheet, about 1” apart.

Bake until bottoms are deeply golden and tops look dry, 13 to 15 minutes.

Let cool completely. Fig bars will keep, in an airtight container at room temperature, up to 3 days, or longer if refrigerated or frozen.