Preheat oven to 350 °F (175 °C).
Butter and flour a 9 inch (23 cm) springform cake pan.
Place a stainless steel bowl over a saucepan filled with simmering hot water.
In bowl, beat eggs and sugar 5 minutes or until mixture thickens.
Off heat, continue beating until mixture cools slightly.
In a second bowl, sift flour and baking powder.
Fold into beaten egg mixture.
With a spatula or whisk, gently fold in melted butter and vanilla extract.
Pour batter into cake pan.
Bake in oven 25-35 minutes Remove from oven.
Detach cake from pan by running a small knife around sides.
Let cool 5 minutes.
Undo cake pan.
Turn out cake onto a wire rack or cookie sheet sprinkled with sugar.
Let stand until cold.