1. Preheat oven to 350°. Pour 1 cup boiling water over dates in a small bowl. Let stand 10 minutes. Drain and pat dry.
2. Lightly beat eggs with a whisk in a large bowl. Whisk in bananas and next 3 ingredients until blended.
3. Stir together brown rice flour and next 4 ingredients in a small bowl. Gently stir flour mixture into egg mixture, stirring just until blended. Gently stir in melted butter, walnuts, and dates. Spoon mixture into a lightly greased 9- x 5-inch loaf pan.
4. Bake at 350° for 1 hour to 1 hour and 10 minutes or until a wooden pick inserted in center comes out clean. Cool in pan on a wire rack 10 minutes. Remove from pan to wire rack, and cool completely (about 1 hour).