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Preheat oven to 350 degrees F. Spray two 9-in. round cake pans with cooking spray and line bottom with parchment paper. Spray parchment paper.
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In large bowl, combine flour, baking powder and salt.
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In separate bowl with electric mixer, beat together sugar and butter until light and fluffy, about 2 minutes. Add vanilla and almond extract and beat until combined.
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Reduce mixer to low speed and alternate adding dry ingredient mixture and buttermilk in 3 additions, beginning and ending with the dry ingredients.
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In separate bowl with electric mixer, beat egg whites to stiff peaks, 4 to 5 minutes. Add big scoop of egg whites to batter and gently fold until just combined to lighten the batter. Add remaining egg whites and fold to combine until no white streaks remain.
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Divide batter between prepared pans. Bake for 35 to 40 minutes, until toothpick inserted in center comes out mostly clean. Remove from oven and cool in pans for 10 minutes. Run knife or offset spatula around edge of cake to loosen, then turn cakes out onto wire rack to cool to room temperature.
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Meanwhile, make frosting. In mixing bowl with electric mixer fitted with whisk attachment, beat together cream cheese, powdered sugar, vanilla and salt on medium-high speed for 3 to 4 minutes, scraping down sides of bowl as necessary, until thickened and smooth.
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Reduce speed to medium-low and add heavy cream in 3 additions. Once cream is incorporated, increase speed to medium-high and beat for 1 minute, until thickened and stiff.
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To assemble cake, use serrated knife to level cakes and carefully slice cakes in half lengthwise to make four layers.
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Place one cake layer on work surface or rotating cake stand. Add dab of frosting to bottom to help hold it in place. Top cake with a thick layer of frosting and sprinkle with peaches. Place second cake layer on top, frost, add peaches and repeat with remaining layers.
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Once all four layers are stacked, cover entire cake with thin layer of frosting, scraping it off so you can see cake through frosting. This is called the crumb coat. Place cake in fridge for half hour to firm up.
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Finish frosting top and sides cake with remaining frosting and decorate with more peaches.