- Preheat oven to 350ºF. Butter 2 large (16 by 14-inch) baking sheets.
- Mix first 6 ingredients in medium bowl. Using electric mixer, beat butter and sugar in large bowl until well blended, about 1 minute. Add egg and molasses; beat until well blended (do not over beat). Add dry ingredients and beat on low speed just until blended. Mix in toffee and crystallized ginger. Chill dough 1 hour.
- Place turbinado sugar in shallow bowl. Using hands, shape dough into 24 balls, each about 1 1/2-inches in diameter. Roll each dough ball in turbinado sugar, coating completely. Place 12 balls on each 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. (Can be made 2 days ahead. Store in airtight container at room temperature.)