Preheat the oven to 350°F (175°C) and grease a 9x13-inch baking pan.
In a medium saucepan, melt the butter over low heat.
Remove from heat and stir in the sugar until well combined.
Allow to cool slightly before adding the eggs, one at a time, mixing well after each addition.
Stir in the vanilla extract.
In a separate bowl, whisk together the flour, cocoa powder, and salt.
Gradually add the dry ingredients to the butter mixture, stirring until just combined.
Fold in the chopped pistachios and chocolate chips.
Pour the batter into the prepared baking pan and spread evenly.
Bake for 25-30 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Let the brownies cool in the pan on a wire rack before cutting into squares.