Prepare the Oven and Pan: Preheat the oven to 350°F. Line the muffin pan or pans with cupcake liners and set aside.
Mix the Cupcake Batter: Add the white cake mix, oil, eggs, water, and pistachio pudding mix to the bowl of a stand mixer. Mix on low speed until the ingredients are combined, scraping down the sides of the bowl as needed. Add the Pistachios: Fold the ½ cup of chopped pistachios into the batter using a spatula, mixing just until the pieces are evenly distributed.
Fill the Cupcake Liners: Use a small ice cream scoop or a ¼-cup measuring cup to divide the batter evenly among the prepared muffin cups.
Bake the Cupcakes: Bake at 350°F for 14–16 minutes, or until the edges are slightly browned and the centers are set. A toothpick inserted into a cupcake should come out clean.
Cool Completely: Remove the cupcakes from the oven and allow them to cool completely before adding the frosting.
Prepare the Pudding Mixture: In a small bowl, combine the milk and 3 tablespoons of pistachio pudding mix. Stir thoroughly until well combined.
Blend the Butter: Place the softened butter and prepared pudding mixture in the bowl of a stand mixer. Mix until the ingredients are fully combined.
Add the First Portion of Sugar: Add about half of the powdered sugar to the butter mixture and mix until smooth, scraping down the sides of the bowl as necessary.
Finish the Frosting: Add the remaining powdered sugar and mix on low speed until incorporated. Increase the mixer speed to medium and continue mixing for 1 minute, until the frosting is fluffy, smooth, and forms soft peaks. Prepare the Piping Bag: Transfer the finished frosting to a piping bag fitted with a large star tip.
Frost the Cupcakes: Once the cupcakes have cooled completely, pipe a generous dollop of frosting onto each cupcake.
Add the Pistachio Topping: Sprinkle additional chopped pistachios over the frosting to finish the cupcakes.
Store the Cupcakes: Keep the cupcakes in an airtight container in the refrigerator for up to 3 days, or freeze them for up to 3 months.