Preheat oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a food processor, grind pistachios until fine.
In a bowl, mix ground pistachios, all-purpose flour, almond flour, baking powder, baking soda, and salt.
In another bowl, beat butter and sugar until fluffy. Add eggs one at a time, then vanilla.
Gradually add dry ingredients to wet, alternating with milk.
Pour batter into pan and bake for 30 minutes or until a toothpick comes out clean.
Cool in pan for 10 minutes, then transfer to a wire rack to cool completely.