Preheat oven to 350°F Line cookie sheet with parchment paper or silicone liner. Place decorating sugar in small bowl and set aside.
In a large bowl whisk together flour, soda, star anise, ground ginger and salt.
Melt butter and stir in molasses, sugar and fresh ginger. Mixture should be warm, but not hot. Let cool if too hot. Whisk in the egg. Pour this over flour mixture, add crystallized ginger and lemon zest. Stir until just combined.
Scoop out dough into small balls (I used small melon baller) and roll in decorating suger to coat. Place on cookie sheets and bake 7 - 10 minutes or until cookies puff up, darken a little, get fragrant and crack.
Note: I "minced" crystallized ginger in food processor as mine was hard, it took awhile, but was very finely minced. I don't know if this would work if it's too soft. Ginger needs to be extremely finely minced.
I also ground the star anise in my spice grinder and then sifted out the larger pieces. Original recipe called for unsulphured molasses; I used cane syrup for a little milder flavor.