1. Using an electric mixer, beat the sugar and butter until smooth. Add the egg, fresh ginger, and lemon zest and beat well.
2. In a bowl, whisk together the flour, ground ginger, cinnamon, baking powder, white pepper, and cloves. Gradually add the dry ingredients to the butter mixture, beating until well combined. Form the dough into a large disk, wrap in plastic, and chill for at least 4 hours or overnight.
3. Preheat the oven to 350°. Scoop out 1 tsp. of the dough at a time and roll it between the palms of your hands to form a ball. Place the balls on a cookie sheet and press down hard with the base of a drinking glass that has been dipped in flour (to prevent sticking) to form thin rounds. Sprinkle the tops of the cookies with turbinado sugar and bake for 8 to 10 minutes, until crisp and browned. Transfer to a wire rack to cool.