Preheat oven to 160°C (325°F) fan. Line your 8-inch cake tin with parchment on the bottom and sides.
In a heatproof bowl, combine eggs, sugar, and vinegar. Warm over simmering water to about 38–40°C (100-104°F), whisking gently to dissolve sugar.
Transfer to a stand mixer and whip on the highest speed for about 8 minutes, until the mixture is thick, pale, and forms ribbons that hold for 2–3 seconds before sinking.
Decrease to medium speed and whip for another 3 minutes. Then decrease to low speed and whisk for 5 minutes.
Rub xanthan gum into sugar between your fingers to ensure it will not clump on contact with the foam. Combine this with all other dry ingredients and vigorously whisk for 1 minute or sift a few times.
Pour the egg foam into a wide mixing bowl. Sift one-third of the dries over the foam and very gently ‘slice and scoop’ to combine.
After about five folds, add another third, repeat, add the last of the dries, and when the dries have nearly disappeared, measure the oil and (optional) vanilla into a small bowl.
Scoop 1-2 tbsp of the batter into the oil and mix to create a ‘liaison’. Continue adding small amounts of batter and mixing until the oil and batter have emulsified.
Pour this evenly over the batter, then gently fold in using the same method.
Pour batter into lined tin. Drop the tin 30-60cm (1-2 feet) above the counter to encourage larger bubbles to pop.
Gently run a skewer in a figure 8 pattern through the batter to distribute the batter evenly and pop bubbles inside.
Bake until the top springs back, a skewer comes out clean, and the sides are just beginning to pull away from the tin. Check at 20 minutes.
Let cool for 10 minutes in tin, then turn out onto a wire rack and cool completely before removing parchment.
