Combine 2 cups of the brandy, 2 cups of the rum, currants, raisins, prunes, cherries, citrus peel, cinnamon, anise, and vanilla bean seeds in a medium pot and bring to a gentle boil. Remove from heat, cover, and let steep for 2 hours.
Preheat oven to 350°. Grease two 8" round cake pans with 1 tbsp. of the butter and set aside. Sift together flour, baking powder, cinnamon, nutmeg, and allspice into a large bowl. Set flour mixture aside. Using an electric mixer, cream the remaining 1 cup butter and brown sugar in a large bowl until fluffy. Add eggs one at a time, beating well after each addition. Add the mixed essence and the vanilla extract and beat until just combined. Set the butter mixture aside.
Drain the steeped fruit, discard cinnamon stick, transfer to food processor, and pulse until it resembles a coarse paste. Transfer the fruit paste to the bowl containing the butter mixture and beat well. Add the flour mixture in 4 batches, beating after each addition. Add the burnt sugar syrup and beat until just combined. Divide batter between the prepared cake pans and bake for 40 minutes. Lower the heat to 250° and bake until a toothpick inserted in middle comes out clean, about 25 minutes more. Let cakes cool on a rack for 20 minutes.
Meanwhile, mix together the remaining 3⁄4 cup brandy, 3⁄4 cup rum, and the sherry in a small bowl. Generously brush the cakes with the brandy mixture (save what remains) and let cool completely. Remove cakes from pans. Wrap them tightly in plastic wrap and then foil and seal in an airtight container. Store in a cool, dry place for at least 3 days before eating. (You may store cakes for up to 3 months. If doing so, use the remaining brandy mixture to rebaste the cakes generously every 7 days. Make another batch of brandy mixture, if necessary.) Cut into wedges to serve.