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Preheat oven to 350 degrees F. Butter and flour a 9" x 9" baking dish; set aside
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In a medium bowl, combine flour, sugar, baking soda, salt, ginger, cinnamon, cloves, and nutmeg.
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In a large bowl, beat together butter and molasses. Add dry ingredients; mix until just combined. Add water, buttermilk, and egg. Mix until well combined, scraping sides of bowl as needed.
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Pour batter into prepared baking dish. Bake for 35 to 40 minutes, or until a toothpick inserted in the center comes out clean. Cool on a wire rack for at least 15 minutes before slicing into 16 pieces.
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While gingerbread is baking, make pudding. In a medium bowl, add vanilla pudding mix, milk, and Coffee-mate. Whisk for 2 minutes. Cover pudding with plastic wrap, touching the surface of the pudding to prevent a skin from forming, and refrigerate until ready to serve.