Preheat oven to 350 degrees. Whisk flour, ground ginger, baking soda, and salt.
Beat butter and granulated sugar with an electric mixer on medium-high speed until pale and fluffy. Beat in egg and egg yolk, then the grated and crystallized gingers. Reduce speed to low. Add flour mixture in 3 additions, alternating with the molasses. Beat until well combined.
Shape teaspoons of dough into balls, and roll in sanding sugar. Space 2 inches apart on parchment-lined baking sheets.
Bake until cookies are flattened and edges are dark golden brown, 12 to 14 minutes. Let cool on sheets 5 minutes, then transfer cookies to wire racks to cool completely. Cookies can be stored in airtight containers for up to 2 days or frozen for up to 1 month.