Preheat oven to 350 degrees F.
Line 2 baking sheets with parchment paper, and set aside. In the bowl of an electric mixer fitted with the paddle attachment, mix butter and sugar on medium-high speed until light and fluffy, about 5 minutes. Scrape down sides of bowl twice. Add egg, and mix on high speed to combine. Add zest, and mix to combine.
In a bowl, whisk together the flour, ground ginger, baking soda, salt, and crystallized ginger, and add it to butter mixture. Mix on medium-low speed to combine, about 20 seconds.
Using 2 spoons, drop about 2 teaspoons of batter on the prepared baking sheets. Repeat until no dough remains, spacing each cookie 2 inches apart. Bake for 7 minutes.
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