Preheat your oven to 350°F (175°C) and line a 13x9 inch baking dish with parchment paper. Set the dish aside for later use. This step ensures your bars will release easily after baking.
In a large bowl, combine the yellow cake mix, 1 large egg, and 1/2 cup melted butter. Fold the ingredients together until a dough forms. Press this dough evenly into the bottom of the prepared baking dish, making sure to cover the entire surface.
In another large bowl, beat together the cream cheese, vanilla extract, and pumpkin pie spice until the mixture is smooth and creamy. Then, add the canned pumpkin puree, 3 large eggs, and another 1/2 cup melted butter, mixing until fully combined. Gradually mix in the powdered sugar until the batter is smooth and thick. I like to sift the powdered sugar before adding to avoid lumps.
Pour the creamy pumpkin mixture from Step 3 over the dough layer pressed into your pan in Step 2. Spread the mixture evenly with a spatula. Bake in the preheated oven for 45 minutes, or until the edges are set and the center is slightly jiggly.
Remove the pan from the oven and let the bars cool completely in the baking dish. Then refrigerate for at least 1 hour to help set the filling before cutting into squares and serving. I find chilling them makes slicing much easier and creates clean edges.