Preheat your oven to 350°F (175°C).
Grease and flour a round cake pan.
In a mixing bowl, beat the eggs and sugar until pale and fluffy.
Sift the flour, baking powder, and salt together.
Gradually fold the dry ingredients into the egg mixture.
Add the melted butter and vanilla extract, mixing gently.
Pour the batter into the prepared pan.
Bake for 25-30 minutes or until a toothpick comes out clean.
Allow the cake to cool in the pan for 10 minutes, then transfer to a wire rack.
Dust with powdered sugar before serving.