Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 9 inch round cake pan.
In a large bowl, beat the eggs and sugar with an electric mixer on high speed until light and fluffy, about 5 minutes.
Sift together the flour, baking powder, and salt, and fold into the egg mixture using a rubber spatula. Add vanilla extract and mix until well combined.
Pour the batter into the prepared pan and bake for 25 to 30 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Cool the cake in the pan for 10 minutes, then turn out onto a wire rack and cool completely before serving.