Whisk together flour, ground ginger, baking soda, cinnamon, cloves, and salt in a medium bowl and set aside.
Beat butter and sugar with an electric mixer until light and fluffy, about 3 minutes, then beat in egg, molasses, and fresh ginger until well combined.
Gradually mix in the dry ingredients until just combined, then cover the dough and refrigerate for at least 2 hours or overnight.
Preheat oven to 350°F and line baking sheets with parchment paper.
Roll dough into 1-inch balls, roll each ball in coarse sugar, and place 2 inches apart on prepared baking sheets.
Bake for 10-12 minutes until edges are set and tops are crackled, then cool on baking sheet for 5 minutes before transferring to a wire rack.