Preheat the oven to 180°C (360°F). Lightly grease a 9-inch round springform cake pan and line the base with baking paper.
Beat the eggs and sugar together in a mixing bowl until thick and pale. Sift in the flour, mixing to combine. Add the vanilla extract and stir until well blended.
Pour into the prepared pan. Bake for 40 minutes, until set and golden brown. Leave the cake to cool.