Step 1: Prepare the Cake Base
Preheat your oven to 350°F (175°C). Generously grease a 9x13-inch baking dish with non-stick cooking spray or butter. In a large mixing bowl, combine the dry yellow cake mix, the melted butter, and one large egg. Use an electric mixer on medium speed or a wooden spoon to mix the ingredients until a thick, cohesive dough forms.Step 2: Press the Crust
Transfer the thick dough into your prepared baking dish. Lightly grease your fingers with butter or cooking spray, and gently press the mixture into an even layer across the bottom of the pan. Actionable Tip: Ensure the crust is pushed slightly up the edges of the pan to create a "wall" that will contain the liquid cream cheese layer you are about to add.Step 3: Whip the Cream Cheese Layer
In a separate, clean mixing bowl, use a hand or stand mixer to beat the softened cream cheese until it is completely smooth and lump-free. Once smooth, add the remaining two eggs and the vanilla extract, beating until well incorporated. Finally, turn the mixer to the lowest speed and gradually add the powdered sugar. Mix just until combined—do not over-whip, or you will incorporate too much air into the custard.Step 4: Layer and Bake
Pour the luscious cream cheese mixture directly over the pressed cake base. Use an offset spatula to smooth it into an even layer. Bake in the preheated oven for 40 to 45 minutes. Pro Tip: The cake is done when the edges are a deep golden brown and slightly puffed, but the very center still has a noticeable "jiggle" when you gently shake the pan. Do not overbake!Step 5: Cool, Dust, and Serve
Remove the cake from the oven and place the pan on a wire cooling rack. This is the hardest part: you must let the cake cool completely (preferably popping it into the refrigerator for at least two hours once it reaches room temperature). Once cooled and set, generously dust the top with extra powdered sugar using a fine-mesh sieve, then cut into squares.