1. To make Cakes: Preheat oven to 350°F. Coat 2 5-cup Bundt pans with cooking spray. Dust with flour.
2. Whisk together flours, baking powder, salt, and baking soda in bowl. Stir in dates and ginger.
3. Whisk together egg replacer and 1 cup water in large bowl. Whisk in sugar, oil, and orange juice. Fold in orange pieces. Stir in flour mixture.
4. Divide batter between prepared pans. Bake 45 minutes, or until toothpick inserted in centers comes out clean. Cool in pans 20 minutes, then unmold.
5. To make Glaze: Whisk together confectioners’ sugar, orange juice, and rum until smooth.
6. Poke holes in Cakes with toothpick. Drizzle Cakes with Glaze, using pastry brush or butter knife to coat evenly.