Preheat oven, prep pans, and sift dry ingredients: Preheat the oven to 375°F. 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.

Cream butter and sugar: In the bowl of an electric mixer fitted with paddle attachment, cream together butter and sugar until light and fluffy, about 2 minutes.

Add extracts: Beat in vanilla and almond extracts.

Add flour and milk: Add the flour mixture in three additions, alternating with the milk and the water, and beginning and ending with the flour. Set batter aside.

Whip egg whites: In a clean bowl of the electric mixer fitted with the whisk attachment, beat egg whites until stiff peaks form.

Fold whites into batter; transfer to pans: Fold gently into reserved batter until well combined. Divide batter between prepared pans.

Bake and cool cakes: 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.

Make fruit and nut mixture for filling: 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.

Cook sugar mixture for frosting: 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°F (soft-ball stage) as measured on a candy thermometer.

Beat egg whites and add sugar mixture: 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°F, 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.

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

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.