Preheat oven to 350° F. Place dates in a small bowl and then pour boiling water over them; let dates stand 10 minutes. Drain; pat dates dry and set aside.
Place eggs in a large bowl and lightly whisk. Add bananas, applesauce, sugar and vanilla; whisk until blended. Set aside.
In a small bowl, combine sorghum flour, brown rice flour, baking soda, nutmeg and salt. Gently combine flour mixture and egg mixture, stirring until just blended. Gently stir in dates, walnuts and melted butter. Spoon bread mixture into a lightly greased 9- x 5-inch loaf pan.
Bake until a wooden pick inserted into the center comes out clean, about 1 hour to 1 hour and 5 minutes. Cool bread in pan on a wire rack for 10 minutes. Remove bread from pan and completely cool on wire rack.