Combine chopped pistachio nuts and flour; set aside. Beat butter, white sugar and lemon zest with an electric mixer on medium high in a medium bowl, until fluffy, 2-3 minutes. Beat in vanilla. Reduce speed to low and gradually add pistachios flour mixture. Chill for 1 hour and up to 2 days.
Preheat oven to 325 degrees. Line 2 baking sheets with parchment paper. Place the powdered sugar in a small bowl. Roll level tablespoons of dough into balls. Place on prepared baking sheets, spacing about 2 inches apart. Bake, rotating the sheets halfway through, until the edges are firm and golden brown, 16-18 minutes. Cool slightly on baking sheets, then toss the warm cookies in powdered sugar to coat. Transfer to wire rack to cool. Makes 40 cookies.