Sift the flour, ground ginger, baking soda, cinnamon, salt, and allspice together into a mixing bowl; stir.
Beat sugar and butter with an electric mixer in a large bowl until smooth and creamy. Beat egg and molasses into creamed butter mixture. Gradually stir flour mixture into butter mixture until just coming together into a batter. Gently fold crystallized ginger through the batter.
Roll rounded teaspoon-sized amounts of dough into small balls between your hands and place onto ungreased baking sheets about 2 inches apart.
Bake in preheated oven until the tops are rounded and slightly cracked, about 10 minutes. Cool cookies on baking sheets for 1 minute before removing to a wire rack to cool completely.
