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For cake: Preheat the oven to 350 degrees F (180 degrees C). Grease 2 (8-inch) round cake pans. Line bottoms with parchment paper. Dust pans with flour, shaking out excess.
Sift together cake flour, baking powder, and salt 3 times in a medium bowl.
Beat egg whites in a large bowl with an electric mixer at medium-low speed until foamy. Gradually add 1/2 cup white sugar; mix until soft peaks form.
In another large bowl, with clean beaters, mix butter with remaining 1 cup white sugar with mixer at medium speed until light and fluffy. Alternately add flour mixture and milk until combined. Mix in vanilla and almond extracts. Fold in egg whites. Divide batter between prepared pans.
Bake in the preheated oven until tops spring back when lightly touched, 35 to 40 minutes. Cool in pans on a wire rack 10 minutes. Remove from pans. Cool completely on wire racks. Trim cake tops with a bread knife to level, if needed. Wrap each layer in plastic wrap and freeze at least 2 hours. (Frozen layers are easier to stack and frost.)
Meanwhile, for frosting, with clean beaters, mix together cream cheese and butter in a large bowl with mixer at medium speed, 30 seconds. Add caramel sauce, vanilla, and salt; mix until light and fluffy. Mix in powdered sugar, 1/2 cup at a time, to reach desired spreading consistency.
For filling, melt butter in a large skillet over medium heat. Add apple and brown sugar. Cook and stir until apple is tender and caramelized, about 8 minutes. Remove from skillet. Cool completely.
For streusel topper: preheat oven to 350 degrees F (180 degrees C). Line a cookie sheet with parchment paper. Combine all-purpose flour, brown sugar, and ci nnamon in a small bowl. Cut in butter with a pastry blender until mixture resembles coarse crumbs. Stir in almonds. Spread on prepared cookie sheet.
Bake in the preheated oven, stirring halfway through, until golden brown, about 10 minutes.
Unwrap cake layers. Place 1 cake layer on a serving platter. Spread with 1/2 cup frosting. Top with apple filling, spreading in an even layer. Top with remaining cake layer. Spread top with 1/2 cup frosting. Spread sides with remaining 3 cups frosting (an offset spatula can make spreading easier). Sprinkle top of frosted cake with streusel topper.
