PreparationMake the cake: Preheat oven to 350°F. Lightly coat two 9"-diameter cake pans with nonstick spray. Line bottoms with parchment paper rounds; lightly coat rounds with nonstick spray. If using raisins and rum, heat together in a small saucepan over low just until warm, about 2 minutes. Remove from heat and let sit until liquid is absorbed and raisins are plump, 15–20 minutes. Meanwhile, toast walnuts on a rimmed baking sheet, tossing once, until golden brown, 8–10 minutes; let cool. Combine carrots and buttermilk in a medium bowl. Whisk flour, cinnamon, ginger, nutmeg, baking powder, salt, and baking soda in a large bowl. Using an electric mixer on high speed, beat eggs, granulated sugar, brown sugar, and vanilla extract until pale and thick, about 4 minutes. Reduce speed to medium-low and gradually stream in oil. Add dry ingredients in 3 additions, alternating with carrot mixture in 2 additions, beginning and ending with dry ingredients; mix until smooth. Fold in raisins, if using, and walnuts with a rubber spatula. Scrape batter into prepared pans. Bake cakes, rotating pans halfway through, until a tester inserted into the center comes out clean, 35–45 minutes. Transfer pans to a wire rack and let cakes cool 10 minutes. Run a knife around sides of cakes and invert onto wire rack; remove parchment. Let cool completely. Make the frosting: Using an electric mixer on high speed, beat cream cheese and butter in a medium bowl until smooth, about 1 minute. Beat in vanilla extract and salt. Reduce speed to low and gradually mix in powdered sugar. Increase speed to high and beat frosting until light and fluffy, about 2 minutes. Assemble the cake: Place 1 cake, domed side down, on a platter. Spread 3/4 cup frosting evenly over top. Place remaining cake, domed side down, on top. Spread top and sides with 1 1/4 cups frosting and chill 30 minutes to let frosting set. Spread remaining frosting over top and sides, swirling decoratively. Top with Candied Carrot Coins, if desired.