Preheat oven to 350 degrees
Line two baking sheets with parchment paper
In a medium bowl, whisk together flour, baking soda, salt, ginger, allspice, and pepper.
With an electric mixer, cream butter, brown sugar, and 1/2 cup granulated sugar until light and fluffy. Beat in molasses and egg. With mixer on low, gradually beat in flour mixture until just combined.
Divide dough into twelve 2-inch balls. Place tough at least 4 inches apart on prepared baking sheets. Flatten into 3-inch rounds. Sprinkle with sugar remaining in bowl.
Bake until brown, rotating sheets halfway through, 12 to 15 minutes. Cool cookies on a wire rack.