Pulse 1/2 cup (60 g) of pistachios in a food processor until they look like coarse sand. Finely chop the other 1/3 cup (40 g) by hand and set aside.
In a large bowl, stir the butter and powdered sugar until smooth and creamy. Mix in the vanilla and salt.
Add the flour, ground pistachios and cornstarch and stir gently until a soft dough forms.
Shape the dough into a log about 2 inches (5 cm) wide and 8 inches (20 cm) long. Roll the log in the chopped pistachios, pressing gently.
Wrap the log in parchment paper and chill for at least 1 hour, until very firm.
Heat the oven to 325°F (160°C) and line a baking sheet with parchment. Slice the log into rounds about 1/3 inch (8 mm) thick and place 1 inch (2.5 cm) apart. Bake for 14 to 16 minutes, until the edges are pale golden.
Cool on the pan for 5 minutes, then move to a wire rack to cool completely.