Preheat the oven to 350°F (175°C). Lightly grease a 13x9-inch baking pan with butter or non-stick cooking spray to ensure easy removal of the cake after baking.

In a large mixing bowl, combine the yellow cake mix, two eggs, melted butter, and vanilla extract. Mix thoroughly until a stiff batter forms. Press this mixture evenly into the bottom of the prepared baking pan to form the base layer.

In a separate bowl, blend together the softened cream cheese, the remaining two eggs, and the confectioners' sugar. Continue mixing until the topping becomes smooth and creamy in texture.

Pour the cream cheese mixture evenly over the cake base layer in the baking pan, ensuring the surface is smooth and level.

Place the pan in the preheated oven and bake for approximately 35 minutes. The cake is done when the edges are lightly golden and a toothpick inserted into the center comes out mostly clean but still slightly moist.

Remove the cake from the oven and allow it to cool in the pan on a wire rack. Once cooled, cut into squares and serve.