Microwave raisins and dark rum for 1 minute, then set aside to soak.
Butter and flour two 9-inch round cake pans and line the bottoms with parchment paper.
Preheat oven to 350°F (175°C).
In a medium bowl, whisk together flour, baking powder, baking soda, salt, and cinnamon.
In a stand mixer, cream sugar and vegetable oil on medium speed for 1 minute.
Add eggs one at a time, mixing well after each. Add applesauce and vanilla, then mix and scrape down the sides of the bowl.
Gradually add dry ingredients to the wet mixture on low speed until just combined.
Stir in grated carrots, crushed pineapple (with juice), and shredded coconut.
Fold in soaked raisins and chopped walnuts by hand.
Divide the batter evenly between the prepared pans.
Bake for 35–40 minutes or until a toothpick inserted in the center comes out clean.
Cool in pans for 10 minutes, then transfer cakes to wire racks and remove parchment while still warm.
To make the frosting, beat softened butter and cream cheese in a large bowl until smooth.
Add vanilla, then gradually beat in powdered sugar until frosting is light and creamy.
Level the cakes if necessary. Place the first cake layer on a serving plate with a small dab of frosting underneath to keep it steady.
Spread a 1/4-inch layer of frosting on top. Add the second cake layer and frost the top and sides.
Use a star tip and pastry bag to pipe decorative borders. Sprinkle the remaining coconut and walnuts over the top.
Serve immediately or refrigerate until ready to enjoy.