Preheat oven to 350 degrees F. Prepare baking sheet with cooking spray.
Mix first flour, ginger, baking soda cinnamon and allspice together in medium bowl. Set aside.
Using electric mixer, cream butter and sugar in large bowl until well blended, about 1-2 minutes. Add egg and molasses and beat until well blended, about 30 seconds. Add dry ingredients and beat on low speed just until blended. Mix in toffee and crystallized ginger. Chill dough 1 hour.
After chilling, shape dough into 24 balls, each about 1 1/2-inches in diameter. Roll each dough ball in turbinado sugar, coating completely. Place balls on prepared sheet, spacing evenly apart.
Bake cookies 8 minutes. Reverse cookie sheets and continue baking until cracked on top but still soft to touch, about 8 minutes longer. Cool cookies on sheets 5 minutes.
Using metal spatula, transfer cookies to racks and cool completely.