Preheat oven to 335°F (168°C). Grease two 8-inch round cake pans with butter or baking spray, line bottoms with parchment paper, and grease the parchment.
In stand mixer bowl, whisk together cake flour, granulated sugar, baking powder, baking soda, and salt until evenly distributed.
Add softened butter and mix on low with paddle attachment until mixture resembles coarse, damp sand, about 1-2 minutes.
In a separate bowl, combine 3/4 cup buttermilk, oil, vanilla, almond extract, and vinegar. Whisk egg whites until frothy and stir into buttermilk mixture.
With mixer on low, pour remaining 1/4 cup buttermilk into butter-flour mixture. Increase to medium and mix for 1 minute until batter thickens.
Gradually pour in buttermilk-egg white mixture with mixer on low. Scrape bowl, increase to medium, and beat for 2 full minutes. Scrape and mix briefly.
Divide batter evenly between prepared pans (about 650-700g each). Tap pans on counter to release air bubbles. Bake 28-35 minutes until toothpick comes clean.
Cool cakes in pans on wire racks for 15 minutes. Run a thin spatula around edges, invert onto racks, peel off parchment, and cool completely (at least 1 hour).
Beat softened cream cheese and butter on medium-high until smooth and fluffy, about 2 minutes. Gradually add sifted powdered sugar, then vanilla and heavy cream. Beat until light and spreadable.
Place first cake layer flat side down. Spread 3/4-1 cup frosting evenly to edges. Top with second layer, flat side up. Apply thin crumb coat, refrigerate 15-20 minutes, then apply final frosting layer.