In a medium bowl, whisk together the instant pistachio pudding mix and cold milk for about 2 minutes until it thickens.
Fold in the whipped topping and vanilla extract until well combined.
In a 9x13-inch baking dish, layer graham crackers on the bottom.
Spread half of the pistachio mixture over the crackers.
Repeat the layers with another layer of graham crackers and the remaining pistachio mixture.
Top with a final layer of graham crackers.
Cover the dish with plastic wrap and refrigerate for at least 4 hours, or overnight for best results.
Before serving, sprinkle the chopped pistachios on top for garnish.
Slice into squares and enjoy!