Preheat your oven to 350°F (175°C).
In a large bowl, cream together the softened butter, granulated sugar, and brown sugar until smooth.
Beat in the eggs one at a time, then stir in the vanilla extract.
In another bowl, whisk together the flour, baking soda, and salt.
Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Fold in the finely chopped pistachios.
Drop tablespoon-sized balls of dough onto a parchment-lined baking sheet.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden.
Allow cookies to cool on the baking sheet for a few minutes before transferring to a wire rack.
Dust with powdered sugar before serving.