Spiced Carrot Layer Cake

Ingredients

• 1 cup unsalted butter, plus more for pans
• 1 1⁄4 cups flour, plus more for pans
• 1 1⁄4 cups whole wheat flour
• 1 tbsp. baking powder
• 1 tbsp. baking soda
• 1 tbsp. ground cinnamon
• 2 tsp. ground ginger
• 1 tsp. kosher salt
• 1⁄2 tsp. ground allspice
• 1 cup sweetened flaked coconut
• 1⁄2 cup finely ground almonds
• 3 cups finely grated carrots
• 1 1⁄2 cups packed dark brown sugar
• 3 eggs, separated
• 1⁄2 cup plain yogurt
• 1⁄4 cup orange juice
• 1 tbsp. orange zest
• 1 tsp. vanilla extract
• 12 tbsp. unsalted butter
• 1⁄2 cup sugar
• 1⁄4 cup buttermilk
• 1 tbsp. light corn syrup
• 3⁄4 tsp. baking soda
• 1 1⁄2 tsp. vanilla extract
• 1⁄2 cup mascarpone cheese
• 3 (8-oz.) packages cream cheese
• 2 tbsp. dark or spiced rum
• 1 (1-lb.) box confectioners' sugar
• 2 cups finely chopped walnuts