Preheat your oven to 350°F. Line a 9x13-inch baking dish with parchment paper, ensuring there's an overhang for easy removal.
In a mixing bowl, combine the yellow cake mix, melted butter, and 1 egg. Mix until a soft dough forms. Press this mixture evenly into the bottom of your prepared dish.
In another bowl, beat the softened cream cheese and softened butter together until smooth and creamy. Add in the remaining egg, egg yolk, vanilla extract, and confectioners' sugar. Mix until well combined and smooth.
Pour the cream cheese mixture over the crust in the baking dish, spreading it out evenly.
Place the dish in the preheated oven and bake for 40-45 minutes. The edges should turn a golden brown, and the center should remain slightly jiggly.
Once baked, remove from the oven and let it cool to room temperature. For best results, refrigerate for at least 2 hours before cutting into bars. Before serving, dust with additional confectioners' sugar for a sweet finish.