Preheat oven to 350F (175C), positioning rack in the lower-middle level and preparing the baking pan.

Sift together the cake flour, 1 tablespoon of sugar, and salt in a bowl.

Melt and clarify the butter, keeping it warm.

In a mixer, beat eggs with remaining sugar and vanilla extract until the mixture forms a ribbon-like consistency when the beater is lifted.

Gently fold in a quarter of the sifted flour mixture into the egg mixture.

Fold in half of the remaining flour mixture, followed by the last portion.

Incorporate a spoonful of the batter into the warm clarified butter to temper it.

Gently fold the butter-batter mixture back into the remaining batter.

Pour the batter into the prepared pan, filling it to no more than 1/4 inch from the rim.

Lightly tap the pan on the work surface to release any trapped air bubbles.

Bake for 30-35 minutes, or until the cake is puffed, lightly browned, and shows slight shrinkage from the pan sides.

Cool in the pan for 20 minutes before inverting onto a wire rack to cool completely.

Allow the cake to cool completely before filling and icing.