Preheat the oven to 400F and set a rack in the middle. Lightly spray a 12×17 baking sheet with parchment paper.
Whisk the eggs, egg yolks, vanilla, salt and sugar together in a large bowl over a pan of simmering water. Whisk gently until the mixture is just lukewarm.
Transfer the mixture to the bowl of a stand mixer fitter with the whisk attachment and whip on medium-high speed until the egg mixture is cooled and tripled in volume.
Over a medium bowl or a piece of parchment paper, sift together the flour and cocoa. Add one-third of the flour mixture to the beaten egg mixture.
Use a rubber spatula to fold in the flour mixture, making sure to scrape all the way to the bottom of the bowl to prevent the flour mixture from making lumps.