In a large bowl, add cold heavy cream. Whip with a hand mixer or stand mixer until medium peaks have formed (about 2 to 3 minutes). Set aside.
In a separate bowl, add pumpkin puree, confectioner's sugar, vanilla extract, and spices. Stir until combined. Gently fold together your whipped cream and pumpkin mixtures until evenly incorporated.
In an 8x8 square pan, add a thin layer of pumpkin mousse (this layer is not repeated). Top with a single layer of graham crackers. Top graham crackers with ⅓ of pumpkin mousse, spread into an even layer. Repeat these layers two more times, for a total of 3 layers each of graham crackers and pumpkin mousse.
Cover and refrigerate for 1 hour for firm graham crackers, or 3 hours for a softer texture. Graham crackers will continue to soften over time and cake is best served within 24 hours.
Slice and serve cold.
Heavy cream, ¼ cup of confectioner's sugar, and 1 teaspoon vanilla extract can be substituted with 4 cups of Cool Whip.
Graham crackers can be substituted with vanilla wafers or Oreo cookies. Thicker cookies take longer to soften, about 12-18 hours.
Spices listed can be substituted with an equal amount of pumpkin pie spice.
To make ahead: prepare pumpkin mousse, cover, and refrigerate overnight. Assemble cake as directed about 3 hours before serving.