WHISK flour, baking soda, ginger, cinnamon, salt and pepper in a medium bowl.
BEAT butter and sugar in a large bowl with an electric mixer on medium until fluffy, about 3 min. Add egg and molasses and beat until combined, then beat in fresh ginger. Stir in flour mixture until combined. Refrigerate at least 1 hr or overnight.
PREHEAT oven to 350F, then line 2 baking sheets with parchment.
SCOOP out 1-tbsp portions of dough and roll into balls. Coat with coarse sugar and arrange 2 in. apart on prepared sheets.
BAKE until browned, 11 to 13 min. Let cool for 5 min, then transfer to a rack to cool. Cookies will keep well for up to 5 days in an airtight container.