In a medium bowl, whisk together flour, baking soda, salt, ginger, allspice, and white pepper. Set aside.
In the bowl of an electric mixer, combine butter with light brown sugar and granulated sugar and beat until light and fluffy. Beat in molasses and egg, and mix well.
Add the reserved dry ingredients, and beat until just combined. Form the dough into a ball and cover with plastic wrap. Refrigerate until firm, at least 2 hours or overnight.
Heat oven to 350 degrees.
Remove dough from refrigerator. Shape dough into 2-inch diameter balls.
Pour sanding sugar into a large bowl, and roll balls in sanding sugar, coating well.
Place cookies on baking sheets (if nonstick, no need to line; if not using nonstick, place cookies on parchment paper). Space cookies 4 inches apart. For flatter, crispier cookies, press down on cookies slightly.
Transfer to oven, and bake until brown, 12-15 minutes. Remove from oven, and transfer to a wire rack to cool.