1. 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.

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

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.

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.

5. Prepare filling: Transfer 1 cup frosting to a medium bowl. Add figs, raisins, and nuts. Stir to combine, and set aside.

6. Assemble cake: Place one layer on a serving plate; spread with filling. Place the second cake layer on top. Spread frosting over the sides and top of the cake.