In food processor, process ½ cup sugar and fresh ginger until combined, about 10 seconds; set aside for rolling.
Heat oven to 375 degrees. Line two large baking sheets with parchment paper.
Whisk wheat starch, xanthan gum, pudding, cinnamon, baking powder and salt in medium bowl; set aside.
In standing mixer fitted with paddle attachment or with hand mixer, beat butter, ¾ cup granulated sugar, and brown sugar at medium speed until light and fluffy, about 3 minutes, scraping down sides of bowl with rubber spatula as needed. Add egg, water, crystallized ginger, and vanilla; beat at medium speed until combined, about 30 seconds. Add dry ingredients and beat at low speed until just combined, about 30 seconds, scraping down bowl as needed.
Place ginger sugar for rolling in shallow bowl. Roll tablespoon dough into 1 -inch ball; roll ball in ginger sugar, then place on prepared baking sheet. Repeat with remaining dough, spacing balls about 2 inches apart on baking sheet.
Bake until cookies are golden brown around edges and just set and very lightly colored in center, about 9 to 12 minutes. Cool cookies on baking sheet about 3 minutes; using wide metal spatula, transfer cookies to wire rack and cool to room temperature.