1. Preheat the oven to 350°F. Generously oil a 9 inch springform pan with olive oil and line the bottom of the pan with parchment or waxed paper. Oil the paper and dust it lightly with flour.
2. In a small saucepan, boil the figs with the brandy for several minutes, until the liquid has cooked off. Set aside to cool.
3. In the bowl of a stand mixer, combine the dry ingredients (sugar through salt). Mix to combine. Add the olive oil, mix well, and then the eggs, beating well after each addition. Add the figs and mix until combined.
4. Pour the batter into the prepared cake pan and bake in the center of the oven until a toothpick comes out clean, 25-30 minutes. Put the pan on a rack and carefully run a paring knife around the inside edge to release the cake. Let cool for 10 min. Using a second rack to sandwich the cake pan, flip the pan over. Carefully lift the pan from the cake, gently peel off and discard the paper liner, and let the cake cool completely before serving with the optional dusting of confectioner's sugar.