Place the softened butter and powdered sugar into a large mixing bowl. Beat until light and creamy. Add the vanilla extract and mix again. This creates the rich and buttery base that gives shortbread its classic texture.

Add the flour and salt to the butter mixture. Mix slowly until a soft dough forms. The dough may look slightly crumbly at first, but it will come together as you continue mixing gently.

Add the finely chopped pistachios to the dough. Stir until they are evenly distributed throughout the mixture. This ensures every cookie gets plenty of nutty flavor and a pleasant crunch.

Turn the dough onto a clean surface. Shape it into a log about two inches wide. Wrap tightly in plastic wrap and refrigerate for at least one hour. Chilling helps the cookies hold their shape.

Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper. Remove the chilled dough from the refrigerator and unwrap it carefully before slicing.

Using a sharp knife, cut the dough into slices about one-quarter inch thick. Arrange the cookies on the prepared baking sheet. Leave a little space between each cookie for even baking.

If desired, sprinkle coarse sugar over the tops of the cookies. This adds a light crunch and a little sparkle. It also gives the finished cookies a bakery-style appearance.

Bake the cookies for 12 to 15 minutes. The edges should look lightly golden. Avoid overbaking because shortbread should remain tender and delicate rather than crisp and dry.

Remove the baking sheet from the oven. Allow the cookies to cool for five minutes before transferring them to a cooling rack. Let them cool completely before serving or storing.