Preheat the oven to 350 degrees. Spray a 9x9 pan with non-stick spray and line it with parchment paper.
Add the pistachios to a food processor and pulse until finely ground.
1 cup (140 g) pistachios (deshelled)
In a medium bowl, whisk together the all purpose flour, baking powder, baking soda, and salt. Then set aside the flour mixture.
2 ¼ cups (281 g) all-purpose flour, spooned and leveled, 1 ½ teaspoon baking powder, ¼ teaspoon baking soda, ½ teaspoon salt
Add the softened butter and granulated white sugar to a large bowl. Cream together for 2 minutes with an electric mixer. (You can also use a stand mixer fit with a paddle attachment.)
10 tablespoon (140 g) unsalted butter, softened, 1 ½ cups (300 g) granulated white sugar
Then add in the eggs and vanilla and mix on medium speed until pale in color and smooth, about 1 minute.
3 eggs, at room temperature, 1 tablespoon (15 ml) vanilla
Add the buttermilk and the dry ingredients to the wet ingredients a little at a time and mix on low speed until the cake batter is combined. Scrape the sides of the bowl with a rubber spatula as necessary.
1 cup (240 ml) buttermilk, at room temperature
Fold in the ground pistachios.
Pour the batter into the prepared baking pan.
Bake the cake for 38-44 minutes, or until a cake tester comes out clean from the center.
Then let the cake cool in the pan on a wire rack until completely cool.