Line an 8 × 8-inch pan with aluminum foil or parchment paper, leaving an overhang for easy removal.
Whisk the cold milk and pistachio pudding mix together for 1 minute. Let the mixture stand for 5 minutes to thicken.
Reserve 1 cup of the whipped topping for the top. Fold the remaining whipped topping into the pistachio pudding until evenly combined.
Arrange 6 graham cracker sheets in the bottom of the prepared pan, breaking them as needed to fit.
Spread half of the pistachio mixture over the crackers. Add another layer of 6 crackers and the remaining pudding mixture.
Finish with the final 6 graham crackers and spread the reserved whipped topping over the top.
Cover and refrigerate overnight, or for at least 8 hours, until the crackers soften.
Garnish with chopped pistachios, cut into squares, and serve chilled.