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

In a large bowl, combine the eggs and granulated sugar. Beat on high speed for 5 to 7 minutes until thick and pale.

Stir in the vanilla extract.

In a separate bowl, sift together the all-purpose flour, baking powder, and salt.

Gently fold the dry ingredients into the egg mixture in three additions to preserve air.

Drizzle the melted butter around the edge, folding it in until just combined.

Pour the batter into the prepared pan and smooth the top.

Bake for 25 to 30 minutes, or until a toothpick inserted comes out clean.

Let the cake cool in the pan for 10 minutes, then turn it out onto a wire rack to cool completely.

Dust with powdered sugar, slice, and serve.