In a medium mixing bowl, combine 1 cup bread flour, yeast, salt and brown sugar.
Heat water, oil, and bananas to 120° to 130°F; add to flour mixture. Blend at low speed until moistened. Add egg; beat 3 minutes at medium speed.
By hand, add dates and gradually stir in enough remaining flour to make a soft dough. Knead on floured surface until smooth and elastic, 5 to 8 minutes.
Place dough in lightly oiled bowl and turn to grease top. Cover; let rise until dough doubles in size.about 45 minutes.
Punch down dough. On lightly floured surface, roll or pat to a 14 x 7-inch rectangle. Starting with shorter side, roll up tightly, pressing dough into roll with each turn. Pinch edges and ends to seal. Place in a greased 9 x 5- bread pan.
Cover, let rise in warm place until indentation remains after lightly touching the side of the loaf, about 30 minutes.
Bake at 375°F for 35 to 40 minutes until golden brown. Remove from pans; cool.