Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a mixing bowl, cream the room-temperature butter and powdered sugar together until light and fluffy, about 3-4 minutes.
Add the vanilla extract and mix well.
In another bowl, combine the all-purpose flour, finely chopped pistachios, ground cardamom, and salt. Mix until well blended.
Gradually add the flour mixture to the butter mixture, mixing just until combined; do not overmix.
Turn the dough out onto a lightly floured surface and shape it into a log, about 2 inches in diameter. Wrap the log in plastic wrap and refrigerate for at least 30 minutes to firm up.
Once chilled, slice the dough into ¼-inch thick rounds and place them on the prepared baking sheet about 1 inch apart.
Sprinkle additional chopped pistachios on top of each cookie for garnish.
Bake for 12-15 minutes or until the edges are lightly golden. Remove from the oven and allow to cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.
Enjoy your Pistachio Cardamom Shortbread with tea or coffee!