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Line two baking sheets with parchment. Chop chocolate into ¼-inch chunks; set aside. In a medium bowl, sift together flour, ground ginger, cinnamon, cloves, nutmeg, and cocoa.
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In the bowl of an electric mixer, fitted with the paddle attachment, beat butter and grated ginger until whitened, about 4 minutes. Add brown sugar; beat until combined. Add molasses; beat until combined.
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In a small bowl, dissolve baking soda in 1 ½ teaspoons boiling water. Beat half of flour mixture into butter mixture. Beat in baking-soda mixture, then remaining half of flour mixture. Mix in chocolate; turn out onto a piece of plastic wrap. Pat dough out to about 1 inch thick; seal with wrap; refrigerate until firm, 2 hours or more.
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Heat oven to 325 degrees. Roll dough into 1 ½- inch balls; place 2 inches apart on baking sheets. Refrigerate 20 minutes. Roll in granulated sugar. Bake until the surfaces crack slightly, 10 to 12 minutes. Let cool 5 minutes; transfer to a wire rack to cool completely.