Melt 2 tablespoons butter in a pan set over medium heat. Add apples and cinnamon, and cook for 5-8 minutes until apples have softened, stirring often.
Transfer apples to a small bowl and set aside to cool.
To make easy caramel sauce:
In the same pan, melt remaining ¼ cup butter and whisk together with brown sugar and heavy cream. Bring to a boil and cook for 1-2 minutes, stirring almost constantly, until sauce starts to thicken.
Remove pan from the heat an stir in vanilla and salt.
Let caramel cool completely to room temperature. To quickly cool caramel, pour it into a small bowl and set that bowl inside a larger bowl filled with ice water and stir constantly for several minutes.
To make creamy filling and assemble ice box cake:
In the bowl of a stand mixer fitted with a paddle attachment, or in a large bowl and a hand-held mixer, beat cream cheese until smooth.
While the mixer is running, add heavy whipping cream a tablespoon at a time to slowly incorporate it into the cream cheese so it stays smooth. Stop and scrape down the bowl as needed. Once enough cream has been added (about ½ a cup) that the mixture is liquid, add the rest all at once. Beat cream mixture on medium high speed until it holds soft peaks.
Add half of the easy caramel sauce and all of the apples to the bowl and gently fold into the whipped cream mixture until combined.
Line a 9x5-inch loaf pan with parchment paper, if desired. Spread an even layer of gingersnap cookies on the bottom of the pan, breaking them into pieces as needed to create a complete layer.
Add ⅓ of caramel whipped cream mixture on top of the gingersnaps and spread into an even layer. Drizzle with more caramel sauce. Repeat 2 more times until there are 3 total layers of gingersnaps, creamy filling, and caramel sauce.
Chill in the fridge for 4-6 hours before serving.
To serve, remove cake from pan with the help of the parchment paper and slice, or scoop cake out of the pan with a spoon. Top servings with a generous drizzle of the remaining caramel sauce.