In a large mixing bowl, cream together the cold butter, brown sugar, pistachio paste, and white sugar until the mixture is well combined and smooth. This may take a few minutes, so be patient and ensure that everything is evenly incorporated before moving on to the next step.
In a separate bowl, mix together the dry ingredients: all-purpose flour, cake flour, baking soda, baking powder, and salt. Once combined, set the mixture aside until ready to use.
Add the egg to the butter and sugar mixture, and mix until fully combined. Then, add the egg yolk and vanilla extract and continue mixing until well incorporated.
Gradually add in the dry ingredients you set aside, mixing until about 80% combined. There should still be some visible streaks of flour in the dough.
Add 2 cups of whole pistachios and gently mix until they are evenly distributed throughout the dough. Be careful not to overmix.
Weigh the dough into 130-145g balls and place them in an airtight container. Let the dough balls sit in the refrigerator for a few hours until hardened, or leave them overnight for best results.