In a medium bowl, combine all the dry ingredients (rice flour through the cream of tartar). Set aside.
In a large bowl, blend the sugar and butter until creamy and lightened in color. Add the vanilla and beat again.
Begin adding the flour mix and the milk to the butter mix, alternating a little of each at once, until it is all incorporated. The batter will be thick.
In another bowl, beat the egg whites until soft peaks form.
Fold the eggs whites into the batter gently, using a scooping gesture to prevent deflating as much as possible.
Pour the batter into two 8" round pans or a 9x13 pan, or maybe 18 - 24 cupcakes.
Bake at 350 for about 20 - 25 minutes (adjusting up for a 9x13). Test with a toothpick in the center to assure it is done.
Once the cake has cooled for 10 or 15 minutes, remove from pans. Serve as desired.