Heat oven to 375° F. Line 2 baking sheets with parchment paper or aluminum foil.
With an electric mixer on medium-high, beat the butter, brown and granulated sugars, corn syrup, and vanilla for 3 minutes. Add the egg and beat until combined. In a separate bowl, whisk together the flour, salt, baking soda, and ginger. Reduce mixer speed to low and slowly add the flour mixture to the egg mixture.
Divide the dough into 2 portions. Wrap in plastic. Freeze for 1 hour. On a floured surface, roll the dough out 1/4 inch thick. Cut into 2-inch stars. Bake for 8 minutes. Cool on the baking sheets for 5 minutes. Transfer the cookies to wire racks to cool completely. Sprinkle with confectioners' sugar.