Preheat oven to 350°F (175°C) and line a 9x9 inch baking pan with parchment paper.
Make the streusel by cutting cold butter into brown sugar, flour, and chopped pistachios until crumbly. Chill in the refrigerator.
Whisk together the dry ingredients: flour, baking powder, baking soda, and salt.
In a large bowl, cream the room-temperature butter and granulated sugar until light and fluffy.
Beat in the eggs one at a time, then mix in the pistachio paste and vanilla extract.
Gently alternate folding in the dry ingredients and the buttermilk, starting and ending with the dry ingredients. Mix until just combined.
Pour half the batter into the pan, add half the streusel, add remaining batter, and top with the rest of the streusel.
Bake for 45-55 minutes until a toothpick inserted into the center comes out clean. Cool before slicing.