Make the soaked spiced dried fruit: In a medium saucepan, combine the raisins, currants, prunes, cherries, cherry brandy, rum, cinnamon stick, and star anise. Cook over medium heat until just boiling, then remove from the heat and let steep for 1-2 hours.
About 20 minutes before making the cake batter, make the burnt sugar syrup: Add the sugar to a small nonstick saucepan over medium-high heat. Let the sugar deeply caramelize, turning almost black and smoking a bit. Reduce the heat to low and carefully pour in the water (it will steam) and stir vigorously to incorporate. Let the syrup remain in saucepan while it cools, about 15 mins. If it hardens too much before using, add a little more water and stir over low heat.
Remove the cinnamon stick and star anise from the soaked fruit mixture. Transfer to a food processor, add the candied citrus peel, and pulse into a chunky paste. Set aside.
Preheat the oven to 350˚F (180˚C). Grease 2 8-inch or 1 10-inch (25 cm) round cake pans.
Make the cake batter: In a medium bowl, combine the flour, cinnamon, nutmeg, allspice, and baking powder. Set aside.
In a large bowl, cream the butter and brown sugar with an electric hand mixer. Once light and fluffy, beat in the eggs, 1 at a time.
With the mixer running, add ⅓ of the flour mixture then ½ of the fruit paste, then another ⅓ of the flour. Switch to a rubber spatula and fold in the remaining fruit paste and flour.
Add the burnt sugar syrup, vanilla, bitters, and sliced almonds. Fold quickly to incorporate so the syrup doesn’t harden.
Transfer the batter to the prepared baking pan(s).
Bake for 1 hour, then reduce the oven temperature to 250˚F (120˚C), and bake for 45 minutes more, until the cake is dark in color and a toothpick inserted in the center comes out clean.
While the cake is baking, make the soaking liquid: In a liquid measuring cup or small bowl, combine the rum, cherry brandy, and sherry.
Let the cakes to cool for 5 minutes, then carefully run a knife around the edges of the pans. Slowly pour the soaking liquid over each of the cakes, a little at a time, allowing it to soak in. (Reserve about ¼ cup for serving) Let the cakes cool completely in the pans.
You can serve the cake immediately, but the flavor improves with time. Wrap the cooled cakes in plastic wrap and refrigerate for up to 2 months. Pour ½ cup of rum over the cake every 7 days to keep moist while storing.
Brush with more of the soaking liquid before slicing and serving.