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Preheat oven to 350°F. Line 13x9-inch baking pan with foil. Spray foil with no stick cooking spray. Mix flour, ginger, cinnamon, baking soda and salt in medium bowl. Set aside.
Beat butter and 3/4 cup of the sugar in large bowl with electric mixer until light and fluffy. Beat in egg until well blended. Gradually beat in flour mixture until well mixed. Stir in molasses and water just until blended. Spread evenly in prepared pan.
Beat cream cheese in large bowl with electric mixer until smooth. Beat in remaining 1/2 cup sugar and vanilla until smooth. Reserve 1/2 cup of the icing; refrigerate remaining icing. Spoon dollops (about 1 teaspoon each) of the reserved icing over batter in pan. With knife or spatula, swirl icing through batter to marbleize.
Bake 30 minutes or until toothpick inserted in center comes out clean. Cool in pan 15 minutes. Lift out of pan using foil. Cool completely on wire rack. Invert and peel off foil. Spread refrigerated icing over top. Cut into bars. Store in refrigerator.