Preheat the oven to 350°F (175°C). Lightly grease a 9×13-inch baking pan.
Separate the egg yolks and egg whites into two bowls.
In a large bowl, whisk together egg yolks, vanilla extract, and milk.
In another bowl, sift together flour, cocoa powder, and baking powder.
Using a stand mixer, beat the egg whites until soft peaks form. Gradually add in the sugar and continue beating until stiff peaks form.
Gently fold the egg yolk mixture and dry ingredients into the whipped egg whites, a little at a time, until fully incorporated.
Pour the batter into the prepared pan and bake for 30 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool completely for 1-2 hours.