Preheat oven to 350℉. Beat the egg whites to stiff peaks. In a separate bowl, sift the gluten free flour, baking powder, and salt. Set both bowls aside.
Whisk the egg yolks and powdered sugar until smooth and pale yellow. Add the melted butter, milk, and vanilla extract. Stir the dry ingredients in. Fold in the whipped egg whites until very few lumps remain. Pour the batter into a greased 8x8-inch pan and bake for 40-50 minutes, or until the center of the cake barely jiggles. Let the cake cool for at least 5 minutes before serving.