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Position a rack in the center of the oven, and heat the oven to 350 degrees F. Butter and flour a 9-by-13-inch baking pan.
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Using a stand mixer fitted with the paddle attachment (or a handheld mixer), cream together the butter and brown sugar for 2 to 3 minutes, or until light and fluffy. (This step will take 5-6 minutes using a handheld mixer.)
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Stop the mixer a few times and use a rubber spatula to scrape the sides and bottom of the bowl and the paddle to release any clinging butter or sugar.
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In a small bowl, whisk together the grated ginger and eggs until blended. On low speed, slowly add the egg mixture to the butter mixture and mix just until combined. Scrape the sides and bottom of the bowl again and beat on medium speed for 20 to 30 seconds, or until the mixture is homogeneous.
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In a medium bowl, sift together the flour, baking powder, salt, ground ginger, pepper, cinnamon, and cloves.
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In another medium bowl, whisk together the molasses, boiling water, and baking soda. It will foam up! On the lowest speed, add about ⅓ of the flour mixture to the egg-butter mixture, and mix until incorporated. Add the rest of the molasses mixture and mix until incorporated. Stop the mixer and scrape the sides of the bowl. Again on the lowest speed, add about half of the remaining flour mixture and mix until incorporated. Add the rest of the molasses mixture and mix until incorporated. Stop the mixer and scrape the sides and bottom of the bowl. Add the remaining flour mixture, mix on low speed for about 1 minute or until the batter is homogeneous. Scrape the batter into the prepared pan.
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Bake for 50 to 60 minutes (I only cooked mine for 45 minutes) or until the top of the cake springs back when lightly pressed in the middle with a fingertip. Let cool in the pan on a wire rack.
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To make the glaze: In a small bowl, whisk together the confectioners’ sugar and enough of the coffee to make a smooth, thick, spreadable glaze.
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While the cake is still warm, spread the glaze evenly over the top. Let the glaze set for at least 1 hour before serving.
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The cake can be stored in an airtight container at room temperature for up to 3 days.
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Makes one 9- by 13-inch cake.