Preheat the oven to 350°F Butter two 8-inch square pans, line them with parchment paper, and set them aside.
In a large bowl, beat the egg yolks, sugar, and vanilla extract until the mixture becomes light yellow and fluffy. Gently stir the flours into the creamed mixture until they are thoroughly incorporated into the batter.
Beat the egg whites until stiff, glossy peak form. Gently stir 1/3 of the whipped egg whites into the sponge cake batter, and then carefully fold the remainder of the egg whites into the mixture.
Carefully fill each prepared pan with the cake batter and bake for 22 to 26 minutes, until the cakes test done in the middle. Invert the cakes onto a wire rack and allow them to cool before serving with fruit and whipped cream.