Combine dried fruits, candied cherries, and candied citrus peel in a large bowl. Pour 1 cup dark rum over the fruit, ensuring all pieces are coated.
Cover tightly and let soak at room temperature for at least 12 hours or overnight, stirring once or twice. The fruits should be plump and have absorbed most of the liquid by morning.
Preheat oven to 300°F (150°C). Grease a 9-inch springform pan or tube pan thoroughly with butter or non-stick spray.
Line the bottom and sides with parchment paper, allowing some overhang for easy removal. Grease the parchment paper as well.
In a large mixing bowl, beat softened butter and brown sugar on medium-high speed for 3-4 minutes until light, fluffy, and pale in color. Scrape down sides occasionally.
Add eggs one at a time, beating well after each addition. Beat for an extra 30 seconds after the last egg until smooth.
In a separate bowl, whisk together flour, baking powder, cinnamon, nutmeg, allspice, and salt until evenly distributed.
Gradually add flour mixture to butter and egg mixture. Mix on low speed or fold by hand until just combined, being careful not to overmix.
Add rum-soaked fruits (with any remaining liquid) and chopped pecans and walnuts. Fold gently but thoroughly until evenly distributed. Batter will be very thick.
Spoon batter into prepared pan, spreading evenly and smoothing the top. Tap pan on counter a few times to remove air pockets.
Bake on middle rack for 2 hours and 30 minutes, or until a toothpick inserted in the center comes out clean. Tent loosely with foil after the first hour if browning too quickly.
Let cake cool in pan for 30 minutes, then remove and place on a wire rack. While still warm, poke holes all over the top with a wooden skewer.
Brush 2-3 tablespoons of rum over the top, letting it soak into the holes. Let cake cool completely before wrapping.
Once completely cool, wrap cake tightly in rum-soaked cheesecloth, then wrap the entire package in aluminum foil or plastic wrap. Store in an airtight container in a cool, dark place.
Once a week for 4-6 weeks, unwrap the cake and brush with 2 tablespoons of rum. Rewrap and return to storage after each feeding. The cake will become more moist and flavorful with each feeding.