Preheat your oven to 350°F (175°C). Line a 9x13 inch baking pan with parchment paper, leaving an overhang on the sides to easily lift the bars out later. Lightly grease the parchment paper.

In a large mixing bowl, combine the yellow cake mix, 1/2 cup melted butter, and 1 large egg. Mix until well combined and a thick, dough-like consistency forms.

Press the mixture evenly into the bottom of the prepared 9x13 inch baking pan. Set aside.

In a separate medium mixing bowl, using an electric mixer, beat the softened cream cheese until smooth and creamy, about 1-2 minutes.

Add the 2 large eggs and vanilla extract to the cream cheese, beating until just combined, about 30 seconds.

Gradually add the 1/2 cup melted butter and beat until fully incorporated, another 1 minute.

Slowly add the 3 1/2 cups powdered sugar, beating on low speed until fully incorporated and the mixture is smooth. Do not overmix; beat only until combined.

Pour the gooey topping mixture evenly over the pressed crust in the baking pan.

Bake for 35-40 minutes, or until the edges are lightly golden brown and the center is set but still slightly jiggly. The center should look very soft and gooey.

Remove from the oven and let cool completely on a wire rack before cutting. This is crucial for the bars to set properly and achieve their signature gooey texture. Cooling may take 1-2 hours at room temperature, or accelerate by chilling.

Once completely cooled, use the parchment paper overhang to lift the bars out of the pan. Place on a cutting board.

Dust generously with 2 tablespoons of powdered sugar before cutting into squares (approximately 24 pieces).