Make the pumpkin layer. In a food processor, combine the pumpkin puree, cream cheese, light brown sugar, cinnamon, pumpkin pie spice, and nutmeg; process until smooth and thoroughly combined. With the machine running, add maple syrup, and continue to process until combined. Set aside.
Beat the cream. In your mixer's bowl, beat 1 cup heavy cream on high speed until stiff peaks form, about 2 to 3 minutes.
Combine and refrigerate. Using a rubber spatula, gently fold the prepared pumpkin mixture into the whipped cream. Refrigerate until ready to use, or for at least 30 minutes.
In the meantime, prepare the whipped cream layer. In your mixer's bowl, combine the heavy cream, vanilla, and sugar. Beat the mixture until stiff peaks form. Refrigerate until ready to use.
Assemble. Spread a little whipped cream on the bottom of a long and narrow plate or in a 9x13 pan.
Layer. Place one single layer of 4 whole graham crackers over the whipped cream. Spread 1/3 of the vanilla whipped cream over the graham crackers. Spread 1/3 of the pumpkin mousse over the whipped cream. Place a single layer of 4 whole graham crackers over the pumpkin mousse.
Keep layering. Continue to layer until you've used up all the ingredients, ending with whipped cream to cover the entire cake. Cover the pan with plastic wrap and place in the freezer for at least 6 hours or overnight.
Finish and serve. Pull the pumpkin icebox cake out of the freezer, top it with chocolate shavings and chopped pecans, cut it, and serve.