In a small bowl, combine the ginger and 1 teaspoon granulated sugar, mixing with fingers to coat; set aside.
In a medium bowl, add the remaining 3⁄4 cup sugar and the orange zest; mix well.
Fill a medium saucepan 1 inch high with water and set a medium heatproof bowl over the top (be sure the bowl does not touch the water). Add the butter and three-quarters of the chocolate to the bowl; cook, stirring occasionally with a heatproof flexible spatula, until just melted (do not overheat).
Remove the bowl and whisk in the sugar-zest mixture; it will be grainy. One by one, add the cold eggs, whisking energetically after adding each for 1–2 minutes. Whisk in the vanilla, salt, and ginger mixture, which will be syrupy. Using a spatula, gently stir in the flour. Add the remaining chocolate, stirring to blend. Place plastic wrap directly against the surface of the dough and chill for at least 3 hours or up to overnight.
Set a rack in the center of the oven and preheat to 350°. If you've refrigerated the dough overnight, let it sit on the counter for 10 minutes.
Line two baking sheets with parchment paper. Put the confectioners' sugar in a bowl.
Using a medium cookie scoop (1 1⁄2–2 tablespoons) or spoon, scoop out level balls of dough and briefly shape into a ball using fingers (do not overwork or the cookies will not have craggly tops); drop into the bowl of confectioners' sugar and toss to coat well. Transfer to the first baking sheet. Repeat until you have 10 cookies, leaving at least 2 inches between the cookies. Cover and refrigerate the remaining dough.
Bake for 8 minutes. Rotate the sheet, then bake again until the dough has spread and cracked, the sides look set, and the centers are a little soft, about 4 minutes more.
Remove and let cool 2 minutes, then carefully transfer the cookies to a cooling rack. Repeat with the remaining dough and the second baking sheet. Cookies are best eaten the day they are made.