Preheat oven to 350 degrees. Mix the cake flour, mesquite flour, sugar, and salt together, and set aside.
Using a mixer, beat the egg whites, cream of tartar, and vanilla until stiff peaks form.
With a rubber spatula, gently fold the dry ingredients into the egg whites.
Line an ungreased 9-by-13-inch pan with parchment paper, pour the batter in, and bake until done, about 30 minutes. Texture will be spongy.
Invert on a rack to cool, in the pan.