Preheat your oven to 350°F (175°C) and grease and flour a round 9-inch cake pan.

In a large mixing bowl, combine room-temperature eggs and granulated sugar. Beat on medium-high speed for about 5 minutes until pale and fluffy.

Sift in the all-purpose flour, baking powder, and salt into the egg mixture. Gently fold until just combined.

Mix the melted butter and vanilla extract, then gradually fold into the batter.

Pour the batter into the prepared pan and smooth the top. Bake for about 30 minutes, or until a toothpick comes out clean.

Once baked, let the cake cool in the pan for about 10 minutes, then turn it onto a wire rack to cool completely.