Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 10-inch Bundt or tube pan.

Process pistachios in a food processor until nuts become smooth and creamy, 7 to 10 minutes, stopping to scrape down sides of bowl as needed. Set aside.

Whisk cake mix and pudding mix together in a large bowl, creating a well in the center.

Add water, eggs, oil, processed pistachios, green food coloring, and pistachio extract into the center of the well. Whisk together until fully combined. Pour batter into prepared pan.

Bake in the preheated oven until the cake springs back when lightly pressed, or a toothpick inserted in the center comes out clean, 50 to 55 minutes.

Cool in the pan for 15 minutes. Turn out onto a wire rack and cool completely.

To make the glaze: Whisk together powdered sugar, heavy cream, and vanilla extract in a small bowl until fully combined.

Spoon glaze evenly over the cooled cake, garnish with chopped pistachios if desired, slice, and serve.