Preheat oven to 325°F (165°C). Beat butter and sugar until pale and fluffy, about 3 minutes, then beat in vanilla.

Whisk flour, cornstarch, and salt, then mix into butter mixture on low. Fold in cranberries and pistachios until dough comes together.

Divide dough in half. Shape into 2-inch-diameter logs, wrap, and refrigerate at least 30 minutes until firm.

Slice logs into ½-inch rounds. Bake on parchment-lined sheets 12 to 14 minutes, until edges are just golden.

Cool on the sheet 5 minutes, then transfer to a wire rack and serve warm or at room temperature.