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Preheat the oven to 325°F. Lightly grease two 9" round cake pans, or two 8" or 9" stoneware shortbread pans, or a combination.
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Combine the butter, salt, sugar, and vanilla in a mixing bowl, and beat till smooth.
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Place 1 cup 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.
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Add this mixture, with the remaining 1 1/3 cups flour, to the butter-sugar mixture. Beat until well combined.
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Divide the dough in half, and press half into each pan, smoothing the surface with your fingers or a pastry roller.
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Prick the dough all over with a fork; this will prevent it from ballooning up or developing air bubbles as it bakes.
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Bake the shortbread till it's golden brown all over, and a bit browner around the edges, about 35 minutes. Remove it from the oven.
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Loosen the edges of the shortbread from the pan, using a table knife 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.
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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.
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Transfer the wedges to a rack to cool.
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Store shortbread, well wrapped, for up to a week; freeze for longer storage. The flavor improves as the shortbread ages.
