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Preheat the oven to 375°F (190°C).
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In a small bowl, combine the orange juice and oats.
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Set aside to soften for 5 minutes.
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In a large bowl, stir together the whole-wheat flour, unbleached flour, and baking powder.
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In a medium bowl, combine the carrots, maple syrup, egg substitute, applesauce, ginger, and vanilla.
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Stir in the oats/orange juice mixture to the carrot mixture.
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Pour over the flour mixture and combine until all the flour is moistened.
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Do not overmix.
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Coat an 8 x 8-inch baking pan with nonstick spray.
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Add the batter.
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Bake for 20 minutes, or until a cake tester inserted in the center comes out clean.
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Let cool before slicing.
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Store tightly wrapped in plastic wrap or a cookie tin.