Step 1: Preheat your oven to 350°F (175°C) and grease a 9-inch springform pan thoroughly.
Step 2: Cream the butter and granulated sugar in a large bowl until the mixture is light, airy, and pale in color.
Step 3: Add the eggs one at a time, beating well after each addition, then stir in the vanilla extract.
Step 4: Sift together the flour, baking powder, and salt, then gradually fold these dry ingredients into the wet batter.
Step 5: Gently fold in the chopped figs and walnuts until just combined, ensuring they are evenly distributed through the cake batter.
Step 6: Pour the batter into the prepared pan and bake for 45-50 minutes, or until a skewer inserted into the center comes out clean.
Step 7: While the cake bakes, combine orange juice, zest, brown sugar, and rum in a saucepan; simmer for 5 minutes until slightly thickened.
Step 8: Remove the cake from the oven, prick the top with a toothpick, and pour half of the warm syrup over the surface.
Step 9: Allow the cake to cool slightly before removing from the pan and serving with the remaining syrup drizzled on top.