In a medium bowl, combine raisins, currants, cranberries and candied lemon & orange peel. Pour rum over and stir until well mixed. Let it sit for 2 ½ hours, stirring often so the fruits can absorb the rum.
Meanwhile, in a small skillet over medium heat, toast ½ cup blanched sliced almonds until lightly brown, about 5 minutes; set aside to cool completely.
In a medium saucepan over medium heat, combine milk, sugar, salt, almond extract and 1 ½ cups of unsalted butter. Stir until sugar is dissolved. Set aside to cool until it reaches about 100ºF (not cooler or hotter).
In the bowl of a stand mixer, combine yeast, water and honey. Stir and let it sit until “very” foamy, about 15 to 20 minutes.
Add 4 ½ cups flour and, with the dough hook attachment, process for 2 minutes on speed 2.
Meanwhile, add vanilla extract to beaten eggs and stir very well.
Add egg mixture to the flour and process for 3 minutes on speed 2, scraping the sides of the bowl as needed.
Add 1/3 of the milk mixture to the flour mixture and process for 1 minute. Repeat 2 more times with milk mixture and flour, scraping the sides of the bowl after each addition. Add 1 tbsp. flour at a time until dough is smooth and elastic (the bounce factor).
Butter a large bowl. Transfer the dough to the bowl and roll around to coat it with butter. Cover with a clean dish towel and transfer to a draft-free area such as the oven (temperature off). Let it rise for 1 ½ hours.
Punch the dough to deflate and add the fruit mixture with its liquid. Add toasted almonds and, using your hands, stir all the ingredients together until well blended.
Transfer the dough to a lightly floured work surface and divide it in 2. Shape each piece into a rectangle, about 5 X 11-inches. Place each log of dough on a separate baking sheet lined with a silicone mat or parchment paper and cover each with a towel. Transfer to the draft-free area and let them rise for 1 hour.
Remove the logs from their draft-free area and preheat oven to 350ºF.
Transfer them to the preheated oven and bake for 35 minutes or until golden brown.
Remove from the heat and let them cool for 20 minutes.