In the bowl of an electric mixer fitted with the paddle attachment, beat the brown sugar, melted butter ( or oil), and molasses on medium speed for 2-3 minutes.
Scrape down the sides. Beat another 2-3 minutes. Turn the mixer to low speed, add the egg, and beat for 1 minute.
Add freshly grated ginger and candied ginger, scrape the sides of the bowl to make sure all is incorporated. Beat for another couple of minutes.
With the mixer still on low, gradually add the flour to the bowl and mix on medium speed for 2-3 minutes. The mixture will be quite firm but should incorporate all the flour.
Either roll dough into 1 1/2-inch ball and then flatten them lightly with your fingers coating them with turbinado sugar, and place on parchment-lined sheet pans. (Or alternately, roll into an l ½ diameter log, wrap in parchment and refrigerate, unit firm, about 1-2 hours.
Slice off equal-sized disks. Roll in raw sugar.)
Bake for 11-12 minutes. The cookies will be crackled on the top and soft inside. Let the cookies cool on the sheets for 1 to 2 minutes, then transfer to wire racks to cool completely.