Line a 9x9 inch baking dish with plastic wrap. Lay one strip across leaving several inches on either side. Lay another strip of plastic wrap going the opposite way, again leaving several inches.
In a large bowl, stir together the pumpkin purée, cinnamon, ginger, nutmeg, and salt.
In another large bowl, add the heavy whipping cream, powdered sugar, and vanilla. Using an electric whisk, start on low until everything is combined then increase the speed to high. Whisk until stick peaks form.
Gently fold in half of the whipped cream into the pumpkin mixture. Then gently fold in the other half just until everything is combined. Be careful not to over stir and deflate the whipped cream.
To the lined pan, add 1/3 of the whipped pumpkin. Then, place one layer of graham crackers until you have an even layer. Break pieces apart if needed.
Add another layer of whipped cream. Then, using a fine-mesh sieve, sprinkle 1 tablespoon of cocoa powder evenly over the whipped pumpkin. Top with another layer of graham crackers.
Finally, add the rest of the whipped pumpkin, followed by 1 tablespoon of cocoa powder, and one last layer of graham crackers. Fold the plastic wrap over the top of the cake to cover it.
Refrigerate for 24 hours before serving.
When you are ready to serve, unfold the plastic wrap. Place a serving tray over the top and flip the whole thing. Gently remove the plastic wrap from the cake.
Again using the fine-mesh sieve, sprinkle 1 tablespoon of cocoa powder evenly over the top.
Notes
Store the icebox cake in an airtight container in the fridge.