Preheat your oven to 350°F (180°C) for a conventional setting. Lightly grease only the bottom of a 9x13-inch baking pan; leave the sides ungreased and unlined to ensure the cake rises properly.
In a mixing bowl, sift together the flour, cornstarch, baking powder, and salt. Stir to combine, then set aside.
Using a stand or hand mixer, beat the egg whites on medium-high speed for 30 seconds until foamy. Gradually add half of the granulated sugar (½ cup or 100 g), continuing to beat until stiff peaks form, about 3–4 minutes. Set this mixture aside.
In a separate large bowl, combine the remaining sugar (½ cup or 100 g) with the warm water. Stir briefly, then add the egg yolks and vanilla extract. Whip this mixture on medium-high speed for 2 minutes until it turns pale and thick. Slowly stream in the vegetable oil while mixing on medium speed until fully incorporated.
Fold half of the whipped egg whites into the egg yolk mixture, using a spatula to gently incorporate them without deflating the mixture. Add the sifted dry ingredients, folding just until combined. Finally, gently fold in the remaining egg whites until the batter is smooth but still airy. Be cautious not to overmix.
Pour the batter evenly into the prepared pan. Drop the pan gently onto your counter twice to release any large air bubbles. Bake for 25 minutes. The cake is done when its surface springs back lightly after being touched.
Immediately after removing the cake from the oven, drop the pan from a height of about 4 inches (10 cm) to release steam. Invert the pan onto a wire rack to cool for 30 minutes, leaving the cake inside the pan during this time.