Step 1: Preheat your oven to 350°F (175°C). Lightly grease and flour a 9x13 inch baking pan.
Step 2: In a large mixing bowl, combine the yellow cake mix, 1 large egg, and the melted butter. Mix until a thick, crumbly dough forms. Press this mixture evenly into the bottom of the prepared baking pan.
Step 3: In a separate large bowl, beat the softened cream cheese and powdered sugar together with an electric mixer until smooth and creamy.
Step 4: Add the pumpkin puree, the remaining 2 large eggs, vanilla extract, and pumpkin pie spice to the cream cheese mixture. Beat until all ingredients are well combined and the mixture is smooth.
Step 5: Carefully pour the pumpkin cream cheese mixture over the cake mix base in the baking pan, spreading it out evenly with a spatula.
Step 6: Bake for 40-50 minutes, or until the edges are lightly golden and set, but the center still has a slight jiggle. This slight jiggle is key to the gooey texture.
Step 7: Remove the cake from the oven and let it cool completely on a wire rack before cutting and serving. For an extra touch, dust with powdered sugar just before serving.