Preheat the oven to 350 degrees F (175 degrees C).
Sift together flour, ginger, baking soda, cinnamon, cloves, and salt for the cookie base in a bowl.
Cream margarine and white sugar in a large bowl with an electric mixer until light and fluffy. Add egg and beat until well combined. Stir in molasses and water. Gradually stir flour mixture into the molasses mixture. Transfer dough to a 9×13-inch pan, patting it down so it covers the entire bottom of the pan.
Bake in the preheated oven until lightly browned, 25 to 30 minutes. Allow to cool completely.
Beat cream cheese, powdered sugar, and brown sugar for the filling in a large bowl with an electric mixer until smooth. Add molasses, ginger, cinnamon, nutmeg, and cloves and stir, scraping down the sides of the bowl, until mixture is smooth. Fold in 3 cups whipped topping until well combined. Spread filling into the cooled cookie base. Cover with plastic wrap and refrigerate until set, at least 4 hours or overnight.
Garnish with remaining whipped topping before serving.
Stabilized whipped cream can be used in place of whipped topping.
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