Preheat oven to 350 degrees F. Grease bottom and 1/2 inch up the sides of one 9x5x3-inch pan; set aside. In a large bowl combine flour, baking powder, baking soda, salt, and ginger. Make a well in center of flour mixture; set aside.
In a medium bowl stir together eggs, bananas, sugar, and oil. Add egg mixture all at once to flour mixture. Stir just until moistened (batter should be lumpy). Meanwhile, toss chopped mango in 1 Tbsp. flour. Fold dates and mango into batter. Spoon batter into prepared pan. Sprinkle Ginger Streusel-Nut Topping over batter.
Bake for about 70 minutes or until a wooden toothpick inserted near the center comes out clean. If necessary to prevent overbrowning, cover loosely with foil for the last 15 minutes of baking. Cool in pan on a wire rack for 10 minutes. Remove from pan. Cool completely on rack. Wrap and store overnight before slicing.
Ginger Streusel-Nut Topping
In a small bowl combine brown sugar and flour. Using a pastry blender, cut in butter until mixture resembles coarse crumbs. Stir in pistachios and crystallized ginger.