Preheat oven to 350°F. Line bottom of 9x13-inch cake pan with parchment paper. Generously grease the sides of pan with butter. Set aside.
In a medium bowl, whisk together cake flour, baking powder, salt, and ½ cup sugar. In a large bowl, whisk together oil, water, vanilla, and yolks. Add dry mixture to wet mixture in three additions. Fold to combine. The mixture will look like very thick cookie dough.
In large bowl, using an electric hand mixer, beat egg whites and cream of tartar at low speed until foamy. Continue to beat a low speed and slowly add remaining ½ cup of sugar one tablespoon at a time. Once all the sugar has been added, increase to medium speed and beat to stiff peaks.
Add egg whites to cake batter in three additions. Fold to combine. Batter will loosen as you add egg whites.
Transfer batter to prepared cake cake. Spread into an even layer. Bake for 30-35 minutes until the top of cake is lightly golden brown and a toothpick inserted in center of cake comes out clean. Let cool in pan for 5 minutes. Run mini offset spatula along the perimeter of cake pan to loosen cake. Allow cake to cool to room temperature