In a medium saucepan, melt the butter and unsweetened chocolate over medium heat, stirring until smooth; let cool for 10 minutes.
Meanwhile, preheat the oven to 350 degrees ; line 2 large cookie sheets with parchment paper. In a large bowl, whisk together the granulated sugar, flour, cocoa, baking powder, baking soda and salt. Whisk the eggs into the butter mixture, then stir into the dry ingredients until incorporated; stir in the ginger and chocolate chips.
Place the confectioners' sugar in a wide bowl. Shape half of the dough into 1-inch balls, then coat with the confectioners' sugar. Place the cookies about 2 inches apart on the prepared cookie sheets. Bake, switching and rotating the pans after about 10 minutes, until the cookies puff and crack, 14 to 17 minutes total. Let cool for a minute before transferring to racks to cool completely. Repeat with the remaining half of the dough.
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