Grind pistachios into fine powder using a blender.
Don't over-blend or you'll get paste.
Set aside for later use.
Combine flour, baking powder, and salt together.
Add the ground pistachios to this mixture.
Stir everything well.
Beat softened butter with sugar until fluffy.
This takes about 3-4 minutes.
The mixture should look light and creamy.
Add eggs one at a time to butter mixture.
Beat well after adding each egg.
Add vanilla extract and mix again.
Alternate adding flour mixture and milk to batter.
Start and end with flour mixture.
Mix until just combined, don't overmix.
Pour batter into greased cake pan evenly.
Bake at 350°F for 30-35 minutes.
Check with toothpick – it should come out clean.