At least 2 days before baking, combine prunes, raisins, currants, cherries, candied peel, rum and brandy in a glass jar or sturdy plastic container; cover tightly; shake or stir occasionally.
When ready to bake, put soaked fruit and almonds in a blender or food processor; work in batches that the machine can handle; grind to a rough paste, leaving some chunks of fruit intact; add a little brandy or wine, if needed, to loosen mixture in the machine.
If burning sugar, place a deep, heavy-bottomed pot over high heat; add 1 cup white or light brown sugar, and melt, stirring with a wooden spoon; stir, letting sugar darken (it will smoke); when sugar is almost black, stir in ¼ cup boiling water (it will splatter); turn off heat.
Pre-heat oven to 250°F; butter three 9-inch or four 8-inch cake pans; line bottoms with a double layer of parchment or wax paper.
In a mixer, cream butter and 1-pound light or dark brown sugar until smooth and fluffy; mix in eggs one at a time, then lime zest, vanilla and bitters; transfer mixture to a very large bowl.
In a separate bowl, combine flour, baking powder and cinnamon; fold dry ingredients into butter mixture; stir in fruit paste and ¼ cup burnt sugar or molasses; batter should be a medium-dark brown; if too light, add a tablespoon or two of burnt sugar or molasses.
Divide among prepared pans; cakes will not rise much, so fill pans almost to top.
Place in pre-heated oven and bake 1 hour; reduce heat to 225°F; continue to bake 2 to 3 hours longer, until a tester inserted in center comes out clean; remove from oven and place on a rack.
While cakes are hot, brush tops with rum and let soak in.
Repeat while cakes cool; they will absorb about 4 tablespoons total.
When cakes are completely cool, they can be turned out and served.
To keep longer, wrap cakes tightly in wax or parchment paper, then in foil; store in a cool, dry place for up to 1 month.