Preheat the oven to 350°F and grease a round cake pan.
Whisk eggs and sugar together until the mixture is pale and fluffy.
Add vanilla extract, then sift in flour, baking powder, and salt. Fold gently to keep the air in.
Pour the batter into the prepared pan and bake for 25–30 minutes, or until a toothpick comes out clean.
Let the cake cool in the pan for 10 minutes before transferring to a wire rack.