Place the cool whip to thaw at room temperature for an hour.
In a bowl, combine 3 cups of whole milk, two packets of vanilla pudding powder, 2 teaspoons of pumpkin pie spice, and 1 can of pumpkin purée ; if you prefer it sweeter, you can add condensed milk at this stage. Mix these ingredients well with a whisk.
Fold in the thawed cool whip.
In a separate bowl, mix the remaining 2 cups of milk with the remaining teaspoon of pumpkin spice.
Add a bit of the cream mixture to the spice.
Add some of the cream mix to the bottom of your 9x13 tray or 10x14 tray.
Dip each Graham cracker in the milk and line the bottom of 9x13 tray.
Once filled, add a layer cream.
Repeat the process with another layer of graham crackers and cream.
Your final layer should consist of cream, resulting in a total of 3 layers of cookies and 3 layers of cream (I prefer leaving about 1½ cups of cream left so I don't oversaturate the dessert, or you can make a 4th layer).
Remove the foil covering off the frosting can and microwave for 20-30 seconds until it slightly melts.
Pour the melted frosting over the top layer of cream and smooth it out evenly.
Refrigerate for 4 hours before serving.