Finely grind the pistachios in a food processor until they are a coarse powder.
In a medium bowl, whisk together the ground pistachios, flour, baking powder, and salt.
In a large bowl, beat the softened butter and granulated sugar together until light and fluffy.
Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract.
Gradually add the flour mixture to the butter mixture, alternating with the 1/2 cup of milk. Begin and end with the flour mixture.
Pour the batter into the prepared baking pan and spread it evenly.
Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for about 10 minutes.