Preheat oven to 350 degrees. Line 2 large cookie sheets with parchment paper.
In a medium saucepan, melt the butter and unsweetened chocolate over low-medium heat, stirring until smooth and being careful not to burn. Let cool for 10 minutes.
In a large bowl, whisk together the granulated sugar, flour, cocoa, baking powder, baking soda, and salt. Whisk the eggs into the cooled butter mixture, then stir into the dry ingredients until incorporated. Finally, stir in the ginger and chocolate chips.
Place the confectioners’ sugar in a wide bowl. Using a small ice cream scoop or your hands shape dough into 1-inch balls, then coat with the confectioners’ sugar.
Place the cookies about 2 inches apart on the prepared cookie sheets. Bake, 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.