In a medium bowl with a mixer on medium-high speed, beat shortening with granulated sugar until fluffy. Scrape down bowl and beat in egg.
In a small bowl, dissolve baking soda in 2 tsp. warm water. Sift flour and ground spices into a medium bowl.
Beat baking soda mixture into shortening, then add flour mixture in alternating batches with molasses and fresh ginger. Cover with plastic wrap and chill 2 to 3 hours and up to overnight.
Preheat oven to 350°. Scoop dough into 1-tbsp. balls. Roll in turbinado sugar.
Set balls on greased baking sheets at least 2 in. apart. Bake until dry-looking around edges, 8 to 10 minutes. Let cool on baking sheets just until set, then transfer to cooling racks.
*Look for "trans fat-free" on the label.
Make ahead: Baked cookies, up to 1 week, airtight at room temperature.