Preheat your oven to 350°F (175°C) and grease a 9-inch round cake pan.
In a medium bowl, whisk together the flour, pistachio pudding mix, baking powder, baking soda, and salt. Set aside.
In a large mixing bowl, cream the butter and sugar together until light and fluffy.
Add the eggs one at a time, beating well after each addition. Then mix in the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, alternating with the milk and sour cream, starting and ending with the dry ingredients. Mix until just combined.
Fold in the chopped pistachios.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 35 minutes or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely before serving.