Preheat the oven to 350°F (175°C). Grease the baking dish or line it with parchment paper for easier removal.
In a large mixing bowl, combine the softened butter, granulated sugar, and brown sugar. Use a whisk or mixer to cream them together until light and fluffy.
Add the eggs and vanilla extract to the butter mixture, and mix until well incorporated.
In another bowl, whisk together the pistachio pudding mix, all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until combined. Do not overmix.
Fold in the chopped pistachios until evenly distributed throughout the dough.
Pour the cookie dough into the prepared baking dish, spreading it evenly. If desired, sprinkle extra chopped pistachios on top for garnish.
Bake in the preheated oven for 20-25 minutes, or until the edges are golden and a toothpick inserted in the center comes out clean.
Allow the cookie bars to cool in the pan for 10 minutes before transferring them to a cooling rack to cool completely.
Once cool, cut into 12 equal bars and serve.