The night before, toss the dried fruit with sherry and let stand, covered, at room temperature.
Cake
Preheat oven to 325°F. Generously grease two 9-inch round nonstick (gray, not black) cake pans. Line bottoms with parchment paper or wax paper, then grease again
Prepare cake as directed, adding 1 ½ teaspoons almond extract to batter with the water. Divide batter evenly in pans; smooth tops with spatula.
Place pans 3 inches apart on middle rack of oven and bake for 25 to 30 minutes, or until a toothpick inserted into the center comes out clean.
Cool cakes in pans on wire rack for 15 minutes. Run sharp knife around edges to loosen cakes, then invert onto separate plates to cool completely before frosting.
Frosting
In a double-boiler over simmering water, beat egg whites, sugar, cream of tartar, and cold water with a portable mixer on medium-high speed for 7 minutes, or until it is glossy and forms soft peaks. Stir in almond extract.
Remove 3/4 cup of the frosting for the filling and stir in the dried fruit and 2 tablespoons of the chopped pecans.
Assemble the Cake
Place one cake layer on a serving plate, topside down, and spread with the filling. Top with the other cake layer, topside up. Spread the sides and then the top of the cake with the frosting, making decorative swirls with a spatula. Sprinkle the top with remaining pecans and serve immediately.