Place the Rice Chex cereal into a very large bowl. Set aside.
In a medium microwave-safe bowl, combine the white chocolate chips, peanut butter (if using), and butter. Microwave in 30-second intervals, stirring well after each, until the mixture is completely smooth.
Stir the instant pistachio pudding mix and vanilla extract into the melted chocolate mixture until fully combined.
Pour the chocolate mixture over the cereal in the large bowl. Gently fold the cereal until every piece is evenly coated.
Place the powdered sugar into a large zip-top bag or a clean bowl.
Add the coated cereal mixture to the powdered sugar. Seal the bag and shake well until the cereal is completely covered in sugar. Alternatively, toss gently in the bowl.
Spread the finished Pistachio Puppy Chow onto a sheet of wax paper or a baking sheet to cool and set.
Break apart any large clumps before serving or storing.
Notes
For a festive look, add a few drops of green food coloring to the melted chocolate mixture before coating the cereal.
If you skip the peanut butter, you may need to add an extra tablespoon of butter to keep the coating smooth.
Store this addictive no-bake mix in an airtight container at room temperature for up to one week.