How to Make It
Prepare gingerbread cake according to package instructions for an 8x8-inch cake. Cool cake for 20 minutes.
Using a wooden dowel or the round handle of a wooden spoon, poke holes over the entire cake surface; be careful to not poke all the way to the bottom of the cake pan.
Combine the sugar and water in a medium saucepan over medium-high heat, stirring until sugar dissolves; bring to a boil, without stirring. Allow the sugar mixture to boil undisturbed until it reaches a deep amber color, washing down the sides of the saucepan with a wet pastry brush if needed to remove any sugar that begins to crystalize on the sides. Remove saucepan from heat and carefully, but vigorously, whisk in cream (the mixture will bubble up and release steam). Stir in 1/2 teaspoon vanilla and salt. Allow mixture to cool about 20 minutes.
Pour cooled caramel over the surface of the cake, allowing caramel to fill the holes and soak into the top of the cake. Let cake stand at room temperature for about 30 minutes.
Combine softened cream cheese, pumpkin puree, butter, and remaining 1 teaspoon vanilla in the bowl of a stand mixer fitted with the whisk attachment; beat on medium-high speed until mixture is creamy and well blended. Gradually add powdered sugar, beating on medium speed and scraping down sides of bowl as needed. Spread cream cheese mixture evenly over cake; sprinkle evenly with crushed cookies.