Mix in the vanilla extract. Gradually add the flour and salt, mixing until just combined. Fold in the chopped pistachios. Divide the dough in half and shape each half into a log about 2 inches in diameter. Wrap tightly in plastic wrap and chill in the refrigerator for at least 1 hour, or until firm.

Slice the chilled dough into 1/4-inch rounds and place on the prepared baking sheet, spacing about 1 inch apart. Press a few extra pistachio pieces or a sprinkle of coarse sugar onto each cookie if desired. Bake for 12–15 minutes, or until the edges are just beginning to turn golden. Let cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.