1Heat the oven to 350°F and arrange a rack in the middle. Coat an (8-inch) cake pan generously with butter, then flour, tapping out any excess flour; set aside.
2Whisk flour, baking powder, and salt in a medium bowl to combine; set aside.
3In the bowl of a stand mixer fitted with a whisk attachment, combine oil, water, vanilla, egg yolks, and 1/2 cup plus 2 tablespoons of the sugar. Whisk on medium speed until mixture is light in color and looks slightly thickened, about 5 minutes. Turn off the mixer and, using a rubber spatula, scrape down the sides of the bowl. Add reserved dry ingredients, turn the mixer to low, and whisk until smooth, about 1 minute. Transfer batter to a large bowl.
4Wash and dry the mixer bowl and whisk attachment. Place egg whites in the bowl and whisk on high speed until soft peaks form (they should droop over like soft-serve ice cream), about 30 seconds. Gradually add the remaining 2 tablespoons sugar and continue whisking until stiff peaks form (they should stand straight up), about 1 minute more. Using a rubber spatula, fold a quarter of the egg whites into the batter until evenly incorporated; gently fold in the remaining egg whites until just combined and no large white streaks remain.
5Pour the batter into the prepared pan. Bake until the surface of the cake is golden brown and springs back when pressed and a toothpick or cake tester inserted into the center comes out clean, about 30 to 35 minutes. Place on a wire rack to cool slightly, about 15 minutes. Carefully run a knife around the perimeter and turn the cake onto the rack to cool completely.