Combine flours, baking soda, ground ginger, cinnamon, salt, and pepper in a small bowl, crushing any lumps. Whisk together butter, 3/4 cup of the coconut sugar, molasses, egg, vanilla, and fresh ginger in a large bowl until well combined. Pour in flour mixture; stir until well mixed. Refrigerate for 30 minutes.
Preheat oven to 350 degrees. Line 2 baking sheets with parchment. Place remaining 1/4 cup coconut sugar in a small bowl. Scoop batter into small balls (a 1-tablespoon cookie scoop is useful for this), roll lightly in coconut sugar, and place on baking sheets, spacing them 1 inch apart. Use the bottom of a glass to flatten cookies slightly.
Bake until golden, 13 to 15 minutes, switching baking sheets front to back and top to bottom halfway through. Let cool on sheets on cooling racks for 5 minutes, then transfer to racks to cool completely.