Preheat oven to 335°F. Grease and line two 8-inch cake pans.

Whisk cake flour, sugar, salt, baking powder, and baking soda. In another bowl, mix egg whites, 3/4 cup buttermilk, 1/4 cup oil, and vanilla.

Cream softened butter into dry ingredients until crumbly. Mix remaining buttermilk with remaining oil and add to flour mixture. Mix 2 minutes.

Add egg mixture in three additions, mixing thoroughly after each. Divide batter into pans and bake 35–40 minutes.

Cool cakes 10 minutes, remove from pans, and chill at least 30 minutes.

For frosting, whisk sugar and flour in a saucepan for 2 minutes. Add milk and cook until thickened. Cool completely.

Cream butter for 1 minute. Add cooled milk mixture spoonful by spoonful. Add vanilla, almond extract, and salt; whip until smooth.

Assemble by layering frosting between cake layers. Apply crumb coat, chill briefly, then frost top and sides.