Preheat oven to 325 degrees. In a large bowl, whisk together flours, brown sugar, baking powder, salt, and anise. In a medium bowl, whisk eggs until they're pale yellow and hold a ribbon for 1 second when whisk is lifted, about 5 minutes. Whisk in zest.
Fold egg mixture into flour mixture until combined. Fold in figs and walnuts. Lightly spray a parchment-lined baking sheet with cooking spray. Divide dough in half on parchment. Spray hands with cooking spray; form each piece of dough into a 2 1/2-inch-wide log. Bake until dough is firm but gives slightly when pressed, about 25 minutes. Transfer sheet to a wire rack and let logs cool 10 minutes. Reduce oven temperature to 300 degrees.
Cut each log on the diagonal into 1/2-inch-thick slices; place slices, cut side up, on sheet. Bake 7 minutes, flip biscotti, and bake 7 minutes more. Transfer to a wire rack to cool completely.