Set the cream cheese on the counter about 1 hour before starting so it softens fully, and thaw the whipped topping in the refrigerator if frozen. Lightly grease or line a 9x13-inch baking dish with parchment, leaving a little overhang for easy lifting.
Snap the 6 graham cracker sheets into rectangles along the perforated lines and keep them nearby.
Beat the softened cream cheese in a large bowl on medium speed for about 1 minute until completely smooth. Add the powdered sugar and vanilla and beat another minute until fluffy with no sugar streaks, scraping down the bowl.
Fold 1 cup of whipped topping into the cheesecake mixture gently until no white streaks remain, then set the bowl aside.
In a second large bowl, combine the cold milk, pumpkin puree, instant vanilla pudding mix, pumpkin pie spice, and cinnamon. Beat for 1 to 2 minutes until smooth, creamy, and slightly thickened.
Let the pumpkin mixture rest for 5 minutes so the pudding can start to set, then fold in 1 cup of whipped topping until light and uniform in color.
Arrange half of the graham cracker rectangles (about 12 pieces) in a single snug layer across the bottom of the dish, breaking extra pieces to fill any gaps. Press down lightly so the layer sits flat.
Spoon half of the cheesecake filling over the crackers in dollops, then spread gently to the edges with an offset spatula, working slowly so the crackers do not slide. Smooth the top level.
Spoon half of the pumpkin pudding mixture on top and spread carefully to the corners with the back of a spoon or offset spatula. Wipe any drips from the sides of the dish for a clean look.
Arrange the remaining graham cracker rectangles over the pumpkin layer, breaking pieces to fill gaps and saving leftover bits for the topping. Spread the rest of the cheesecake filling over the crackers, then finish with the rest of the pumpkin filling, smoothing the surface neatly.
Spread the remaining whipped topping evenly over the pumpkin layer all the way to the edges. Sprinkle crushed leftover graham cracker bits and chopped pecans over the top, then drizzle the caramel sauce in a zigzag pattern.
Cover the dish tightly with a lid or plastic wrap and refrigerate for at least 4 hours, or overnight, so the graham crackers soften and the layers set.
Run a sharp knife under hot water and wipe it dry. Cut into 15 squares, wiping the knife clean between cuts, and lift each square out with a spatula. Serve with extra caramel on the side.