Add flour, baking soda, sea salt, ground ginger and ground star anise to a large bowl, whisking to combine. Add butter to a small saucepan set over medium-low heat, and warm until just barely melted. Take the saucepan off the heat, and stir in sugars, fresh ginger and molasses. Let the mixture cool until just warm to the touch, then whisk in the egg. Pour the wet mixture into the bowl with the dry ingredients, stirring until combined. Don’t overwork the dough here. Cover the bowl, and let chill in the refrigerator for 2 hours.