Position a rack in the upper third of the oven and a second rack in the lower third then preheat to 375°F. Line 2 large baking sheets with parchment paper.
In a large bowl, sift together the flour, baking soda, and salt.
In the bowl of a stand mixer fitted with the paddle attachment, combine the butter, sugar, and brown sugar and beat on medium speed, scraping the bowl occasionally, until light and fluffy, about 5 minutes.
Add the egg and vanilla and beat until combined, about 2 minutes. With the mixer on low, add the flour mixture in 3 batches, stirring until just combined.
Add the bittersweet and semisweet chocolate chips and the candied ginger and fold until just incorporated. Cover with plastic wrap, pressing the plastic directly on the dough's surface, and chill at least 2 hours and up to 2 days.
Drop the dough by heaping 2 tablespoons onto the baking sheets, leaving about 2 inches between cookies.
Bake, switching the cookies between the upper and lower racks about halfway through baking, until golden brown, 12 to 15 minutes. Cool the cookies on baking sheets for 5 minutes before transferring to a wire rack to cool completely. Continue baking cookies on cooled baking sheets. DO AHEAD: The cookies can be baked ahead and stored, in an airtight container at room temperature, up to 3 days.
