Preheat your oven to 350°F (175°C) and grease a round cake pan.
In a mixing bowl, beat the eggs and sugar together until pale and fluffy.
In another bowl, sift together the flour, baking powder, and salt.
Gently fold the dry ingredients into the egg mixture.
Incorporate the melted butter and vanilla extract into the batter.
Add the milk and mix until smooth.
Pour the batter into the prepared cake pan.
Bake in the preheated oven for 25-30 minutes, or until a toothpick comes out clean.
Remove from the oven and let cool in the pan for 10 minutes.
Transfer to a wire rack to cool completely before serving.