Preheat the oven to 350°F. Spray a 9x9 pan with non-stick spray and line it with parchment paper.
Grind the pistachios in a food processor until finely ground.
In a medium bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, cream together softened butter and granulated white sugar until fluffy.
Add eggs and vanilla, mixing until pale and smooth.
Alternate adding buttermilk and dry ingredients to the wet ingredients, mixing until combined.
Fold in ground pistachios.
Pour batter into the prepared pan and bake for 38-44 minutes, or until a cake tester comes out clean.
Let the cake cool completely in the pan on a wire rack.