In a food processor, grind the pistachios with 1/4 cup of the flour until finely ground, about 30 seconds. Add the remaining flour, sugar, and salt; pulse to combine.

Add the cold butter and vanilla; pulse until coarse meal with pea-sized butter bits remains, about 10 to 12 pulses.

Turn the mixture onto a surface and gently press into a dough. Divide in half, roll into 1 3/4-inch logs, wrap in plastic, and refrigerate at least 2 hours.

Preheat oven to 325°F. Slice logs into generous 1/4-inch rounds, place on parchment-lined sheets, and bake 12 to 14 minutes until edges are pale gold.

Let cool on the sheet for 2 minutes, then transfer to a wire rack to cool completely before serving.