01 - Preheat oven to 350°F. Lightly grease a 9x13-inch baking pan with butter or cooking spray, or line with parchment paper for easy removal.
02 - In a large mixing bowl, combine the yellow cake mix, melted butter, and 1 egg. Stir with a wooden spoon or mix on low speed until a soft, cohesive dough forms. The mixture will be thick and slightly sticky.
03 - Transfer the dough to the prepared pan. Using your hands or the back of a spoon, press the dough evenly across the bottom of the pan to create a uniform base layer. Set aside.
04 - In a separate bowl, beat the softened cream cheese with an electric mixer until completely smooth and creamy, about 1-2 minutes. Add the 2 eggs one at a time, mixing well after each addition. Scrape down the sides of the bowl as needed.
05 - Reduce mixer speed to low and gradually add the powdered sugar, mixing until fully incorporated. Add the lemon juice, lemon zest, and vanilla extract. Continue mixing until the filling is smooth, fluffy, and free of lumps, about 1-2 minutes.
06 - Pour the lemon cream cheese mixture evenly over the base layer in the pan. Use a spatula to spread it into an even layer. Bake for 35-40 minutes. The edges should be set and lightly golden, while the center remains slightly jiggly—this creates the characteristic gooey texture.
07 - Remove from the oven and let the cake cool completely in the pan, at least 1-2 hours. The center will set as it cools. Once fully cooled, cut into 12 squares. Dust with additional powdered sugar before serving, if desired.