Line the bottom of a half pan (18 by 13 inch) with parchment paper. Preheat oven to 350 F and set a rack to the center of the oven.
Place the egg yolk in a medium bowl, add the sugar and whisk until it becomes pale in colour. Add in the milk, water, and oil. Whisk until the lquid is cohesive. Sift in the dry ingredients - cake four, cocoa powder, baking powder, and salt. Whisk until the mixture becomes smooth and shiny. Do not overmix, otherwise the cake might become dense and dry.
Place the egg whites in a stand mixer bowl. Whip the egg whites with a whisk attachment on high until the egg whites become frothy. You can also use a hand mixer for this. Sprinkle in the sugar in three addtions, mixing throughly before adding the next. Whip the egg whites and sugar to a soft peak stage - when you lift up the whisk the tips should be firm but falls back slightly.
When the egg whites are ready, mix in a third of it into the flour mixture with a whisk until the batter is cohesive. Lightly fold in the rest of the egg whites using a rubber spatula until well combined. Careful not to overmix to deflat the batter too much.
Pour the batter into the prepared pan, spread and smooth the batter with an offset spatula or a bench scraper. Bake the cake in the preheated oven for 12-15 minutes until the cake is set. You can test the center with a toothpick, if it comes out clean, it is ready. Cool the cake before assembling.