Preheat oven to 350°F. Spray two 8x4 inch loaf pans with baking spray.

In a medium bowl, combine the gluten free flour, baking soda, and salt. Set aside.

In a large bowl, cream the softened butter and brown sugar until light and fluffy. Add egg whites, mashed bananas, vanilla extract, and mix well.

Gradually add the dry ingredients to the banana mixture, mixing just until combined. Fold in chopped walnuts.

Pour the batter evenly into the prepared loaf pans. Bake for 50 minutes or until a toothpick inserted into the center comes out clean.

Allow to cool in the pans for 10 minutes, then transfer to wire racks to cool completely before slicing.