Five-Spice Gingersnaps

Whisk together flour, five-spice powder, baking soda, and salt in a small bowl.
Pulse ginger with 1/4 cup sugar in a food processor until finely ground.
Add syrup, butter, egg, and remaining 3/4 cup sugar to processor and blend until mixture is thick and creamy, about 3 minutes. Add flour mixture and pulse just until a dough forms. Form dough into a disk and chill, wrapped in plastic wrap, at least 8 hours to allow flavors to develop.
Put oven rack in middle position and preheat oven to 325°F. Line 2 large baking sheets with parchment paper.
Quarter dough. Keeping remaining 3 pieces wrapped in plastic wrap and chilled, roll out 1 piece of dough on a lightly floured sheet of wax paper with a lightly floured rolling pin to 3/4 inch thick. (If dough becomes too soft to roll out, chill on wax paper until firm.) Cut out rounds with cutter and transfer to 1 lined baking sheet, arranging cookies about 2 inches apart.
Bake cookies until slightly puffed and a shade darker, 10 to 12 minutes. Cool 5 minutes on sheet. If desired, make holes with piping tip near edges to hang cookies, then transfer cookies (still on parchment) to a rack to cool completely. (Cookies will flatten slightly as they cool.)
While first batch is baking, roll out and cut another batch, arranging cookies on second lined sheet. Bake in same manner, then gather scraps and chill until dough is firm enough to reroll, 15 to 20 minutes. Make more cookies with scraps (reroll scraps only once) and remaining pieces of dough, cooling sheets and lining them with fresh parchment before using.
If using icing and coloring it, transfer small batches of icing to small bowls, 1 for each color, and tint with food coloring. Spoon each color of icing into a separate pastry bag, pressing out excess air. Twist bag firmly just above icing, then decoratively pipe icing onto cookies. Let icing dry completely (about 1 hour, depending on humidity) before serving or storing cookies.