Preheat the oven to 355F (180C). Line an 11 x 16-inch (28 x 40 cm) jelly roll pan with parchment paper so the bottom and sides are covered. Use nonstick silicone-coated parchment, a Teflon mat, or a perforated silicone mat. Alternatively, fold parchment paper to create a pan of the required size with sides about 1 inch (2 cm) tall, then place it on a baking sheet.
In a large bowl, combine the egg yolks, milk, oil, and vanilla extract. Whisk until well mixed.
Sift in the flour and salt. Whisk until smooth and no dry ingredients remain.
In another bowl, add the egg whites, cream of tartar, and sugar. Whip with a hand mixer, gradually increasing the speed, until medium peaks form.
Fold one-third of the egg white mixture into the egg yolk mixture until combined.
Add the remaining egg whites and gently fold until the batter is homogeneous.
Pour the batter into the prepared pan and spread it evenly using an offset spatula. Bake for 12–15 minutes, or until the top just begins to turn lightly golden.
Remove from the oven and let rest for 1 minute. Turn the cake out onto a fresh sheet of parchment paper and carefully peel off the parchment from the bottom.
Allow to cool completely and cut into two even pieces before assembling.