Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large mixing bowl, cream together the softened butter and powdered sugar until light and fluffy.
Add the rosewater and mix until well combined.
In a separate bowl, whisk together the all-purpose flour, cornstarch, and salt.
Gradually add the dry ingredients to the butter mixture, mixing until just combined.
Fold in the finely chopped pistachios until evenly distributed throughout the dough.
Divide the dough in half and shape each portion into a log about 1 inch in diameter. Wrap each log in plastic wrap and refrigerate for at least 30 minutes.
Remove the logs from the fridge and slice them into ¼ inch thick cookies. Place the cookies on the prepared baking sheet, leaving space between each one.
Bake in the preheated oven for 15-18 minutes or until the edges are lightly golden.
Once baked, allow the shortbread to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.
Once cooled, dust with extra powdered sugar for an elegant finish.