Preheat to 325°F. Line and lightly grease a 9-by-13-inch rimmed quarter-sheet pan.
Whisk all dry cake ingredients together. In another bowl, combine the buttermilk, water, cake vanilla, cake almond extract, and vinegar.
Beat cake butter and granulated sugar on medium for about 3 minutes until creamy. Add the whole egg after incorporating the oil and corn syrup.
On low speed, add dry and wet mixtures alternately in thirds, mixing just until smooth.
Beat the 2 egg whites with cream of tartar in a clean bowl until stiff peaks hold. Fold into the batter in 2 additions, then spread evenly in the pan.
Bake for 18 minutes at 325°F, then lower to 300°F and bake for 6–8 minutes more. Add 1–6 minutes if needed, until the center is set and a tester shows moist crumbs without wet batter.
Cool the cake completely before decorating, allowing about 1 hour.