To begin, preheat the oven to a temperature of 350 F. Before adding any ingredients, make sure to grease and line the bottom of an 8-inch square pan with parchment paper.
Next, sift the cake flour into a separate bowl. To the bowl, add one tablespoon of sugar and a dash of salt, then whisk the mixture together until combined. Repeat the sifting process two more times.
Moving on to the eggs and remaining sugar, add both ingredients to the bowl of a stand mixer. Use the whisk attachment to beat the mixture at medium speed until it becomes fluffy, thick, and pale in color. The mixture should be tripled in volume, similar to that of softly whipped cream.
Add in the vanilla extract and mix gently using a rubber spatula.
When adding the flour mixture to the eggs and sugar mixture, add it in three different additions. To avoid losing volume, gently fold in the flour mixture rather than mixing it too vigorously.
In a separate large mixing bowl, add the melted butter. Scoop about one cup of the batter and mix it into the butter. Stir until the mixture is well incorporated and then fold it back into the remaining batter.
Once everything is combined, pour the batter into the prepared baking pan and bake for approximately 17-20 minutes or until a toothpick inserted into the middle of the cake comes out clean. After baking, allow the cake to cool slightly in the pan before transferring it to a wire rack to cool completely.