Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round pan or line the bottom with parchment.

In a large, clean bowl combine the eggs and granulated sugar. Beat on high speed for 5 to 7 minutes until the mixture is thick, pale, and ribbons form when the beaters are lifted. Stir in the vanilla extract.

Sift the flour, baking powder, and salt into a separate bowl to remove lumps and aerate.

Fold one third of the dry ingredients into the egg mixture using a spatula. Cut through the batter and turn it over gently. Repeat with the remaining dry ingredients in two more additions. Keep the motion light to preserve air.

Drizzle the cooled melted butter around the edge of the batter. Fold it in just until combined, using minimal strokes.

Pour the batter into the prepared pan and smooth the top. Bake for 25 to 30 minutes, or until a toothpick inserted near the center comes out clean.

Remove the cake from the oven and let it cool in the pan for 10 minutes. Turn the cake out onto a wire rack to cool completely.

Dust with powdered sugar, slice, and serve.