Preheat the oven to 325°F. Lightly grease two 9" round cake pans, or two 8" or 9" stoneware shortbread pans, or a combination., In a mixing bowl or bowl of your stand mixer, combine the butter, salt, sugar, and vanilla. Beat untill smooth., Place 1 cup (120g) of the flour in a food processor with the crystallized ginger. Process until the ginger is finely minced; this may take up to 1 minute., Add this mixture, along with the remaining 1 1/3 cups (160g) flour, to the butter-sugar mixture. Beat until well combined., Divide the dough in half (about 385g each) among the two prepared pans. Press into an even layer, smoothing the surface with your fingers or a pastry roller., Prick (dock) the dough all over with a fork; this will prevent it from puffing up or developing air bubbles as it bakes., Bake the shortbread untill it's golden brown all over, and a bit browner around the edges, about 35 minutes. Remove it from the oven., Loosen the edges of the shortbread from the pan using a table knife, a small offset spatula, or heatproof nylon spatula. Wait just a minute or two, then turn the shortbread out of the pan onto a piece of parchment or a clean work surface., Use a bench knife, a knife, or (easiest) a rolling pizza cutter to cut each round into 12 wedges. Do this immediately, while the shortbread is still warm. If you wait, it'll be difficult to cut., Transfer the wedges to a rack to cool., Store any leftover ginger shortbread, well wrapped, for up to a week; freeze for longer storage. The flavor improves as the shortbread ages.