Preheat oven to 350 degrees with rack in center. Whisk together flour, cornmeal, baking powder, and salt.
Put butter in the bowl of an electric mixer fitted with the paddle attachment; mix on medium speed until smooth. Add sugar and mix until pale and fluffy. Mix in eggs one at a time, until well combined. Reduce speed to low. Add flour mixture all at once; mix until just combined. Add lemon zest, cranberries, and pistachios and mix until combined.
Transfer dough to a baking sheet lined with parchment paper. Pat into a log that is roughly 14 by 3 1/2 inches. Bake until firm, lightly browned, and slightly cracked on top, 30 to 35 minutes. Let cool on sheet on a wire rack, about 15 minutes.
Transfer log to a cutting board. Using a serrated knife, cut on the diagonal into 1/2-inch-thick slices. Arrange slices on a baking sheet lined with parchment. Bake cookies, rotating sheet halfway through, until they begin to brown at edges, 15 to 18 minutes.
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