Beat first 4 ingredients at medium-high speed with an electric mixer 30 seconds. Add egg white and fresh ginger; beat 1 minute. Sift together flour and next 6 ingredients. Add flour mixture to butter mixture; beat at low speed 30 seconds. Scrape bowl; fold in crystallized ginger.
Divide dough into 2 disks; wrap tightly in plastic wrap. Chill 4 hours to 3 days. Unwrap 1 dough disk; generously flour both sides. Place between 2 pieces of parchment paper, and roll to 1/8-inch thickness. Chill 30 minutes. Repeat with remaining dough disk.
Cut chilled dough with a 2 1/2-inch round cutter; place cookies 2 inches apart on parchment paper-lined baking sheets. Chill 15 minutes.
Preheat oven to 350°. Bake, in batches, 12 minutes. Rotate pans front to back; bake 4 more minutes. (Cookies will puff up and collapse.) Cool completely on parchment paper on wire racks.