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Preheat oven to 350 degrees.
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Line 13×9-inch baking pan with foil.
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Spray foil with no stick cooking spray.
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Mix flour, ginger, cinnamon, baking soda and salt; set aside.
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Beat butter and 3/4 cup of the sugar in large bowl with electric mixer until light and fluffy.
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Beat in egg until well blended.
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Gradually beat in flour mixture until well mixed.
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Stir in molasses and water just until blended.
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Spread evenly in prepared pan.
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Beat cream cheese in large bowl with electric mixer until smooth.
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Beat in remaining 1/2 cup sugar and vanilla extract until smooth.
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Reserve 1/2 cup of the icing; refrigerate remaining icing.
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Spoon dollops (about 1 teaspoon each) of the reserved icing over batter in pan.
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With knife or spatula, swirl icing through batter to marbleize.
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Bake 30 minutes or until toothpick inserted in center comes out clean. Cool in pan 15 minutes.
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Lift out of pan using foil.
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Cool completely on wire rack.
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Invert and peel off foil.
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Spread refrigerated icing over bars.
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Cut into bars.
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Store in refrigerator.