Separate the egg whites from the egg yolks and place the whites in the bowl of a stand mixer. Preheat the oven to 350 degrees F (177 C). Line two baking trays with parchment paper. Flip the parchment over, and trace the bottom of a 8x8 inch square pan on both pieces of parchment. Flip them back over so the pencil lines won't touch the sponge.
Add half of the sugar (54 grams/¼ cup) to the stand mixer with the egg whites and whip on high speed until stiff peaks form. Add the vanilla and mix until just combined. Transfer the meringue to a large mixing bowl. In the stand mixer (no need to wash it), add the egg yolks and remaining sugar and whip on high until pale and fluffy.
Add a third of the meringue to the whipped yolks and gently fold until fully combined, being careful not to deflate the air whipped into the meringue. Add the second third of the meringue and fold until mostly combined. Add the remaining meringue, sift in the GF flour and salt, and carefully fold until everything is combined, but still light and airy.
Gently transfer the batter to a large piping bag fitted with a large round tip, and pipe to create two squares using the traced marks on the parchment. Use all the batter between the two squares. Bake in the preheated oven for 12-17 minutes, or until the edges are golden brown. Remove from the oven and let the cake squares cool completely at room temperature.