Preheat the oven to 350°F (175°C). Grease a 9x13-inch baking pan or line it with parchment paper.

In a large mixing bowl, combine the yellow cake mix, 1 egg, and the melted butter. Mix until a thick dough forms. Press the dough evenly into the bottom of the prepared pan to form the crust.

In a separate bowl, beat the cream cheese until smooth. Add the remaining 2 eggs and vanilla extract, and mix until fully combined. Gradually add in the powdered sugar, mixing until smooth and creamy.

Pour the cream cheese mixture over the crust and spread it evenly with a spatula.

Bake for 40–45 minutes, or until the edges are golden and set but the center is slightly jiggly—it will firm up as it cools. Don’t overbake; the gooey center is the signature feature!

Let the cake cool completely before cutting into squares. Optionally, dust with more powdered sugar before serving. Gooey butter cake can be stored at room temperature for 1 to 2 days if it's tightly covered with plastic wrap or kept in an airtight container. For longer storage, up to 5 days, place it in the refrigerator and allow it to come to room temperature before serving if you prefer a softer texture.