Preheat your oven to 350°F (175°C). Generously grease a 9x13 inch baking pan with cooking spray or softened butter, coating the corners and sides thoroughly.
Add the cake mix, pumpkin puree, eggs, vegetable oil, water, pumpkin pie spice, cinnamon, and vanilla extract to a large bowl. Beat with an electric mixer on medium speed for 2 minutes until smooth, scraping down the sides halfway through — the batter will be slightly thicker than standard box cake batter.
Pour the batter into the prepared pan, spread evenly to the edges, and bake on the center rack for 28 to 32 minutes until the top springs back when touched and a toothpick inserted in the center comes out with just a few moist crumbs.
Let the cake cool for exactly 10 minutes, then use the handle of a wooden spoon or a thick straw to poke holes all over the surface about 1 inch apart, pressing about halfway to three-quarters of the way through — work all the way to the edges and corners.
In a medium bowl, whisk together the sweetened condensed milk, caramel sauce, and pumpkin pie spice until fully smooth and combined.
Slowly pour the filling evenly over the entire surface of the warm cake, using a spatula to spread it and gently press it into the holes. Let the cake sit at room temperature for 15 minutes before refrigerating.
Cover the pan loosely with plastic wrap (without pressing it onto the surface) and refrigerate for a minimum of 2 hours, or overnight for best results — do not add the whipped topping before chilling.
Spread the thawed whipped topping evenly over the chilled cake, dust with ground cinnamon, and optionally drizzle with caramel sauce, chopped pecans, or toffee bits before slicing and serving.