Preheat the oven to 350°F (175°C). Stir together 1 cup flour, 2 tablespoons granulated sugar, and 1 cup chopped pecans. Cut in the softened butter until the mixture holds together in coarse, damp crumbs.
Press the mixture firmly and evenly into the bottom of a 9x13-inch dish using the flat bottom of a measuring cup. Bake for 18 to 20 minutes, until the edges are light golden brown.
Set the crust on a rack and cool completely, about 30 minutes. Do not add any layer while it is warm.
In a large bowl, beat the softened cream cheese on medium speed until smooth, with no lumps. Add the powdered sugar and vanilla extract, then beat until creamy.
Using a rubber spatula, gently fold in 1 cup of the whipped topping until just combined. Spread evenly over the cooled crust with an offset spatula, sealing it to the edges of the pan. Refrigerate while you make the next layer.
In a separate bowl, whisk the 2 boxes of instant vanilla pudding mix with the 3 cups cold whole milk for about 2 minutes, until it starts to thicken. Add the full can of pumpkin puree and the pumpkin pie spice.
Whisk until the color is even and the mixture is smooth and thick. Spread the pumpkin layer gently over the chilled cream cheese layer, taking care not to pull the layer beneath it.
Spread the remaining whipped topping (about 2 cups) over the pumpkin layer in an even sheet. Scatter the reserved 1/2 cup chopped pecans over the top.
Cover loosely and refrigerate for at least 4 hours, or overnight, until fully set. Drizzle with caramel sauce just before serving, if using, then cut into squares.