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1
For the Cake: Set oven rack in middle position. (If oven is too small to cook both layers on a single rack, set racks in upper-middle and lower-middle positions.) Heat oven to 350 degrees. Spray two 9-inch round cake pans with nonstick cooking spray; line the bottoms with parchment or waxed paper rounds. Spray the paper rounds, dust the pans with flour, and invert pans and rap sharply to remove excess flour.
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2
Pour milk, egg whites, and extracts into 2-cup glass measure, and mix with fork until blended.
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3
Mix cake flour, sugar, baking powder, and salt in bowl of electric mixer at slow speed. Add butter; continue beating at slow speed until mixture resembles moist crumbs, with no powdery streaks remaining.
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4
Add all but 1/2 cup of milk mixture to crumbs and beat at medium speed (or high speed if using handheld mixer) for 1 1/2 minutes. Add remaining 1/2 cup of milk mixture and beat 30 seconds more. Stop mixer and scrape sides of bowl. Return mixer to medium (or high) speed and beat 20 seconds longer.
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5
Divide batter evenly between two prepared cake pans; using rubber spatula, spread batter to pan walls and smooth tops. Arrange pans at least 3 inches from the oven walls and 3 inches apart. (If oven is small, place pans on separate racks in staggered fashion to allow for air circulation.) Bake until thin skewer or toothpick inserted in the center comes out clean, 23 to 25 minutes.
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6
Let cakes rest in pans for 3 minutes. Loosen from sides of pans with a knife, if necessary, and invert onto wire racks. Reinvert onto additional wire racks. Let cool completely, about 1 1/2 hours.
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7
For the Frosting: Beat butter, confectioners' sugar, vanilla, milk, and salt in bowl of electric mixer at slow speed until sugar is moistened. Increase speed to medium-high (high if using handheld mixer); beat, stopping twice to scrape down bowl, until creamy and fluffy, about 1 1/2 minutes. Avoid overbeating, or frosting will be too soft to pipe.
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8
For the Filling: Before assembling cake, set aside 3/4 cup of the frosting for decoration. Spread small dab of frosting in center of cake plate to anchor cake, and set down one cake layer. Combine 1/2 cup of remaining frosting with almonds in small bowl and spread over first layer. Carefully spread jam on top, then cover with second cake layer. Spread frosting over top and sides of assembled cake. Pipe reserved frosting around perimeter of cake at the base and the top. Cut the cake into slices and serve.
