Preheat oven to 350°F (180°C). Spray a 9-inch springform pan with baking spray with flour. Line bottom of pan with parchment paper.
Using a knife or fork, finely chop or mash half of figs. Cut remaining figs into ¼-inch pieces; in a small bowl, toss together ¼-inch fig pieces and 2 tablespoons (16 grams) flour.
In the bowl of a stand mixer fitted with the paddle attachment, beat sugars and oil at medium speed until sandy, 1 to 2 minutes, stopping to scrape bottom and sides of bowl. Add eggs, one at a time, beating until thickened after each addition, about 2 minutes. Add mashed figs and lemon zest; beat until well combined, 1 to 2 minutes, stopping to scrape bottom and sides of bowl.
In a large bowl, whisk together salt, baking powder, cinnamon, nutmeg, allspice, and remaining 3¼ cups (406 grams) flour. In a small bowl, stir together 1 tablespoon (15 grams) warm water and baking soda; stir in buttermilk and vanilla bean paste. With mixer on low speed, gradually add flour mixture to sugar mixture alternately with buttermilk mixture, beginning and ending with flour mixture, beating just until combined after each addition. Using a spatula, fold in ¼-inch fig pieces. Spread batter into prepared pan.
Bake until a wooden pick inserted in center comes out clean, 1 hour and 20 minutes to 1½ hours, loosely covering with foil during final 20 minutes of baking to prevent excess browning. Let cool in pan on a wire rack for 10 minutes. Remove from pan, and let cool completely on a wire rack.
Just before serving, pour Bourbon Caramel Sauce onto cooled cake. Garnish with figs, if desired. Refrigerate in an airtight container for up to 3 days.