Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a large bowl, cream together the butter and sugar until light and fluffy.
Beat in the eggs one at a time, then stir in the vanilla extract.
Combine the flour, baking powder, and salt; gradually mix into the batter.
Stir in the milk until the batter is smooth.
Fold in the chopped pistachios.
If desired, add a few drops of green food coloring to achieve a pistachio color.
Pour the batter into the prepared pan and spread it out evenly.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then remove from the pan and cool completely on a wire rack.