Step 1: Preheat your oven to 350°F (175°C). Lightly grease a 13x9-inch baking pan.
Step 2: In a large mixing bowl, combine the yellow cake mix, 1 large egg, and the melted butter. Mix with a spoon or electric mixer on low speed until the mixture is crumbly but well combined.
Step 3: Press the cake mix mixture evenly into the bottom of the prepared 13x9-inch cake pan, forming the crust. Set the pan aside.
Step 4: In a separate medium bowl, combine the powdered sugar, 3 large eggs, and the softened cream cheese. Beat with an electric mixer until the mixture is completely smooth and creamy, with no lumps of cream cheese remaining.
Step 5: Carefully spread the smooth cream cheese mixture evenly over the cake mix crust in the pan.
Step 6: Bake in the preheated oven for 35 to 40 minutes, or until the topping is set, lightly golden around the edges, and just slightly jiggly in the center. Do not overbake.
Step 7: Remove the pan from the oven and allow the bars to cool completely on a wire rack before slicing them into individual bars. Cooling completely is crucial for the gooey texture to set properly.