Preheat the oven to 325°F.

Butter the bottom and sides of an 8-inch round cake pan that's at least 2 inches deep. Line the bottom with parchment paper and grease. Dust the sides and parchment paper with flour and tap out the excess.

In a medium saucepan, combine the dried fruit, brown sugar, coffee, and butter. Bring to a boil over medium heat. Continue to boil for 3 minutes. The butter will melt, the brown sugar will dissolve, and the dried fruit will plump. Take the pan off the heat and set it aside for 5 minutes to cool slightly.

Sprinkle in the baking soda; the mixture will bubble and foam. Carefully stir the mixture with a silicone spatula. Add the flour, cinnamon, nutmeg, cloves, allspice, baking powder, and salt to the saucepan. Stir with a silicone spatula just until combined and no lumps of dry flour remain.

Scrape the batter into the prepared pan and smooth the top. Bake until a toothpick inserted in the center of the cake comes out clean or with a moist crumb or two attached (no wet batter), about 30 minutes.

Let the cake cool in the pan for 10 minutes. Run a butter knife around the edge of the cake, then turn it out onto a rack to cool completely, peeling off the parchment. Dust the top of the cake with powdered sugar and serve.

Store the cake, covered tightly, at room temperature for up to a week. The cake can be frozen for up to 3 months.