In a large mixing bowl, whisk together the pumpkin purée, brown sugar, pumpkin pie spice, and cinnamon until smooth. Add the instant pudding mix and cold milk, continuing to whisk until the mixture thickens, about 2 minutes.
In a separate bowl, beat the heavy cream until soft peaks form. Gently fold the whipped cream into the pumpkin mixture until fully combined. Set aside in the refrigerator.
If the caramel sauce is too thick, warm it slightly until pourable. If desired, stir in a pinch of sea salt for a salted caramel version. Allow to cool to room temperature.
In a clean bowl, whip together the heavy cream, powdered sugar, and vanilla extract until soft peaks form. Keep this whipped topping chilled until ready to use.
To assemble, place a spoonful of crushed cookies at the bottom of each serving glass or jar. Spoon over a layer of the pumpkin mousse, followed by a light drizzle of caramel sauce. Repeat the layering process until the glass is nearly full.
Top each portion with a generous swirl of whipped cream. Garnish with extra caramel and a sprinkle of cookie crumbs.
Refrigerate the assembled trifles for at least 1 hour before serving to allow the layers to set and the flavors to develop.