Before you start, check your applesauce. If there is any liquid pooled on the surface, spoon it off and discard it. You want the applesauce as thick as possible so it does not make the whipped cream runny. Set it aside.

Pour the very cold heavy cream into a large mixing bowl or the bowl of a stand mixer. Add the brown sugar, cinnamon, and vanilla. Whip on medium-high speed until firm peaks form. This means when you lift the beater, the cream holds a peak that stands straight up without flopping over. Be careful not to over-whip into butter.

Add the thick applesauce and the ground ginger to the whipped cream. Use a rubber spatula to fold gently, turning the bowl and folding from the bottom up. You want the mixture to be fully combined but still light and airy. A few pale streaks of applesauce are fine; overmixing deflates the cream.

Spread a thin layer of the cream mixture across the bottom of your 9x13 dish. This helps the first layer of crackers grip the dish. Lay graham cracker sheets in a single, even layer over the cream, breaking pieces to fill any gaps along the edges.

Spread about one-third of the remaining cream mixture over the crackers in an even layer, going all the way to the edges. Add another layer of graham crackers on top. Repeat this layering, cream then crackers, two more times, finishing with a final layer of cream on top. You should have roughly 3 layers of crackers and 4 layers of cream.

Smooth the top layer of cream with a spatula and sprinkle the crushed graham crackers or cinnamon sugar evenly across the surface. Dust lightly with nutmeg if you like. Cover the dish tightly with plastic wrap and refrigerate for at least 6 hours. Overnight is better and gives clean slices.

When ready to serve, use a sharp knife to cut the cake into squares or rectangles. The crackers will have softened completely into tender, cake-like layers. Serve cold, straight from the refrigerator.