Allow eggs, butter, and egg white for cake layers to stand at room temperature for 30 minutes. Meanwhile, preheat oven to 350 degrees F. Grease and flour two 8x1 1/2-inch round cake pans; set aside.
For Carrot Cake Layer, in a large bowl stir together flour, baking soda, cinnamon, and ginger; set aside. In a medium bowl combine egg, carrots, brown sugar, walnuts, oil, and buttermilk. Add egg mixture to flour mixture; stir until combined. Pour batter into one of the prepared pans, spreading evenly. Bake for 22 to 25 minutes or until a wooden toothpick inserted near the center comes out clean.
For Coconut Cake Layer, in a small bowl stir together flour and baking powder; set aside. In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add granulated sugar and vanilla. Beat until combined, scraping sides of bowl occasionally. Add egg and egg white; beat just until combined. Alternately add flour mixture and coconut milk to butter mixture, beating on low speed after each addition just until combined. Stir in coconut. Pour batter into the remaining prepared pan, spreading evenly. Bake alongside carrot cake layer for 30 to 35 minutes or until a wooden toothpick inserted near the center comes out clean.
Cool cake layers in pans on wire racks for 10 minutes. Remove layers from pans; cool completely on wire racks.
Meanwhile, for Raisin-Rum Filling, in a small saucepan bring rum just to boiling over medium-high heat. Remove from heat. Stir in raisins. Let stand, covered, for 5 minutes. Drain, discarding rum. Set raisins aside. In the same saucepan combine evaporated milk, brown sugar, butter, and egg yolk. Cook and stir over medium heat until thickened and bubbly (165 degrees F). Stir in raisins, coconut, walnuts, and vanilla; cool. Cover and chill until needed.
To assemble, place carrot cake layer, bottom (flat) side up, on a serving platter. Spread with Raisin-Rum Filling. Top with coconut cake layer, top (rounded) side up. Spread top and sides with Cream Cheese Frosting. Sprinkle with toasted walnuts and, if desired, toasted coconut. Chill for 30 minutes before serving. Store any leftover cake, covered, in the refrigerator for up to 3 days.
Cream Cheese Frosting
Allow cream cheese and butter to stand at room temperature for 30 minutes. In a large mixing bowl beat cream cheese, butter, and vanilla with an electric mixer on medium speed until light and fluffy. Gradually beat in powdered sugar to reach spreading consistency.