Step 1

Make the cake: Preheat the oven to 375 degrees. Butter and flour two 9-by-2-inch round pans; set aside. Into a medium bowl, sift together flour, baking powder, and salt three times; set aside.

Step 2

In the bowl of an electric mixer fitted with the paddle attachment, cream together butter and sugar until light and fluffy, about 2 minutes. Beat in vanilla and almond extracts. Add the flour mixture in three additions, alternating with the milk and the water, and beginning and ending with the flour. Set batter aside.

Step 3

In a clean bowl of the electric mixer fitted with the whisk attachment, beat egg whites until stiff peaks form. Fold gently into reserved batter until well combined.

Step 4

Divide batter between prepared pans. Bake until a cake tester inserted in the center comes out clean, about 30 minutes. Transfer pans to a wire rack to cool for 10 minutes. Remove cakes from pans, and return to the rack to cool, top-sides up.

Step 5

Make the filling and frosting: Bring raisins, dates, and rum to a boil in a small saucepan over medium heat, stirring occasionally, until liquid has been absorbed. Remove from heat; let cool. Stir in walnuts; set aside.

Step 6

In a small saucepan, combine sugar, corn syrup, and the water. Bring to a boil over high heat, stirring to dissolve the sugar. When sugar has dissolved, continue to cook without stirring, until it reaches 238 degrees (soft-ball stage) as measured on a candy thermometer.

Step 7

Meanwhile, in the bowl of an electric mixer fitted with the whisk attachment, beat egg whites, vanilla, and salt until stiff peaks form. When sugar mixture has reached 238 degrees, pour it into the beaten egg whites while beating constantly on high speed, until the mixture is cool and is the proper consistency for spreading, about 7 minutes.

Step 8

Transfer 1 cup frosting to a medium bowl. Add reserved dried fruit and nut mixture. Stir to combine, and set aside.

Step 9

Assemble the cake: Trim cake tops. Slice cakes in half horizontally. Place one cake layer on a serving plate; spread with one-third of the filling. Repeat with 2 more cake layers. Top with remaining cake layer, bottom side up. Spread frosting over sides and top of the cake.