Preheat an oven to 350°F, and set an oven rack in the middle position. Line 2 baking sheets with parchment paper.

In a large bowl, whisk together flour, baking soda, star anise, ground ginger, and salt.

Warm butter in medium saucepan until just barely melted. Stir in molasses, sugar, and fresh ginger. The mixture should be warm, but not hot at this point. If it is hot to touch let it cool a bit. Whisk in the beaten egg, then add the wet ingredients into the dry ingredients along the crystallized ginger and lemon zest. Stir until just combined.

Spread turbinado sugar out on a plate. Using your hands, roll a level tablespoon of cookie dough into a ball, then place onto the plate with the sugar. Roll dough ball around in the sugar until it's completely coated. Repeat with remaining dough. Place dough balls on the parchment-lined baking sheets at least 1-inch apart. Working in batches (I always do 1 sheet at a time), bake until cookies are puffed, slightly darker and just starting to crack (10 - 12 minutes). Transfer cookies to a wire rack to cool.