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Preheat oven to 350F. Line a baking sheet with parchment paper.
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In a mixing bowl, stir together flour, sugar, baking powder, and salt. Beat in eggs, one at a time, and vanilla. Fold in dried cranberries and pistachios. The dough will be sticky.
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Scrape dough onto the prepared baking sheet and flatten into a long, wide log, about 10 inches by 5 inches.
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Bake until firm, about 40 minutes. Remove to a wire rack and cool for about 10 minutes. Use a serrated knife to slice into ¾" slice. Transfer back to the pan, cut side down, and bake for another 20 minutes or until golden brown.
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Cool completely before dipping in chocolate.
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Melt white chocolate chips over low heat in a small saucepan, stirring the entire time. Remove from heat and quickly dip the bottoms of each biscotti in white chocolate. Let firm up on a wire rack before serving.