Prepare the oven and tin: Preheat oven to 180°C (355°F). Grease and line the cake tin with parchment.
Warm the eggs and sugar: Place eggs and sugar in a heatproof bowl over simmering water, whisking until lukewarm (not hot).
Whip the eggs: Using a mixer, beat the eggs and sugar until pale, thick, and tripled in volume (ribbon stage).
Add flour: Sift flour with pinch of salt in small batches over the egg mixture, gently folding with a spatula to avoid deflating.
Incorporate butter and vanilla: Mix a spoonful of batter into the melted butter, then fold back into the main mixture with vanilla.
Bake: Pour into prepared tin and bake 25–30 minutes until golden and springy to the touch.
Cool: Remove from oven, cool in the pan for 5 minutes, then transfer to a rack.
Use as base: Slice horizontally and soak layers with syrup before filling with cream, fruit, or ganache.