If the cookies expand while baking, trim the edges with a 1 1/2-inch round cutter while they're still hot.
Pulse butter, sugar, and salt in a food processor until smooth. Add flour and pulse until a dough forms. Stir in pistachios. Shape dough into two 12-inch, 1 1/4-inch diameter logs, tightly wrap in plastic and freeze until firm, 30 minutes.
Preheat oven to 350 degrees, with racks in upper and lower thirds. Cut dough into 1/4-inch slices and transfer to parchment-lined baking sheets. Bake until cookies are set and barely golden at edges, 10 to 12 minutes. Let cool completely on sheets on wire racks. Cookies can be stored in an airtight container at room temperature up to 1 week.