FOR THE FRUIT MIXTURE:
1¼ cups/170 grams dried cherries
1⅓ cups/170 grams dried apricots, cut into 1-centimeter pieces
1⅓ cups /170 grams prunes, cut into 1-centimeter pieces
¾ cup/113 grams dried cranberries
¾ cup/113 grams dried currants
½ cup/113 grams dark rum or brandy
½ cup/113 grams fresh orange juice
FOR THE BATTER:
8 ounces/226 grams unsalted butter, at room temperature, plus more for the pan
2 cups/270 grams all-purpose flour, plus more for the pan
1½ cups/170 grams walnuts or pecans
1½ teaspoons kosher salt (such as Diamond Crystal) or ¾ teaspoon coarse kosher salt (such as Morton’s)
1½ teaspoons ground ginger
¾ teaspoon baking powder
½ teaspoon ground allspice
¼ teaspoon baking soda
Pinch of ground cloves
¾ cup/165 grams packed dark brown sugar
2 teaspoons finely grated lemon zest
1 teaspoon finely grated orange zest
7 ounces/200 grams almond paste
4 large eggs, at room temperature
2 teaspoons vanilla extract
FOR THE ASSEMBLY:
⅓ cup/76 grams dark rum or brandy
⅓ cup/107 grams apricot preserves
1½ cups/165 grams confectioners’ sugar
2 tablespoons milk
1 teaspoon lemon juice
Pinch of kosher salt
Make the fruit mixture: The day before you bake the cake, combine the dried cherries, apricots, prunes, cranberries, currants, rum and orange juice in a medium bowl and fold thoroughly to combine. Cover the bowl tightly and let sit at room temperature until the fruit is soft and has absorbed all (or nearly all) of the liquid, stirring once or twice, 12 to 24 hours.
Arrange an oven rack in the center position and heat the oven to 325 degrees. Generously brush the inside of a 12-cup Bundt pan with butter. Dust the inside of the pan with several pinches of flour, then tap the pan on the counter at different angles to coat every buttered surface. Tap out the excess, then set the pan aside.
Scatter the walnuts (or pecans) across a sheet tray and transfer to the oven. Toast until the walnuts are golden brown and fragrant, shaking the pan halfway through, 8 to 10 minutes. Let cool completely on the baking sheet, then chop the walnuts. Set aside.
In a medium bowl, whisk together the flour, salt, ginger, baking powder, allspice, baking soda and cloves. Set aside.
In a large bowl, combine the butter, brown sugar, lemon zest and orange zest. Pinch off small pieces of the almond paste and add to the bowl. Using a hand mixer, beat the mixture on medium-low until combined, then increase the speed to medium-high and continue to beat, scraping down the sides once or twice, until the mixture is light and fluffy, about 3 minutes.
With the mixer on low, add the eggs one at a time, increasing the speed just to incorporate each egg before decreasing to low and adding the next, until the mixture is very smooth. Beat in the vanilla, then, on low speed, add the flour mixture and mix just until it disappears. Tip in the fruit mixture, along with any unabsorbed liquid, along with the chopped nuts; use a flexible spatula to fold the batter several times, scraping the sides and bottom of the bowl, until the fruit is evenly distributed.
Scrape the batter into the prepared Bundt pan, distributing it evenly all the way around and taking care not to form large air pockets. Smooth the surface, then bake the cake until the surface is golden brown, risen and cracked, and a cake tester inserted into a crack comes out clean, 1 hour 10 minutes to 1 hour 20 minutes. Let the cake cool in the pan for 15 minutes.
Use a skewer or toothpick to poke holes all over the surface of the cake. Use a pastry brush to generously soak the cake with about half of the rum. Let the cake absorb the rum for a few minutes, then turn it out onto a wire rack. Poke more holes all over the cake and dab the remaining rum across every surface.
Warm the apricot preserves in a small saucepan over medium-low heat, stirring often with a heatproof flexible spatula, just until the preserves are fluid. Pass the preserves through a fine mesh sieve into a small bowl, pressing on the solids with the spatula to extract as much of the liquid as possible (discard the solids, or scrape back into the jam jar). Use the pastry brush to paint the strained jam over the cake, covering every surface. Let the cake sit uncovered until it’s completely cooled and the jam is set (it should be slightly tacky but not wet to the touch).
In a medium bowl, combine the confectioners’ sugar, milk, lemon juice and a pinch of salt, and whisk slowly to combine, then whisk vigorously until you have a thick, smooth icing. Slowly pour the icing onto the tallest part of the cake all the way around, letting it slowly cascade down the side. Let the cake sit until the icing is completely set, about 1 hour.
The cake will keep, covered at room temperature, for 1 week.