Preheat the oven to 350°F (175°C).
In a mixing bowl, combine the yellow cake mix, melted butter, and 1 egg. Mix until well combined.
Press the mixture into the bottom of a greased 9x13-inch baking dish to form the crust.
In another bowl, beat the softened cream cheese until smooth.
Add 2 eggs, powdered sugar, and vanilla extract to the cream cheese. Mix until fully incorporated.
Pour the cream cheese mixture over the crust in the baking dish.
Drizzle the remaining melted butter over the top of the cake.
Bake for 40-45 minutes, or until the edges are golden and the center is just set.
Remove from the oven and allow to cool for at least 15 minutes.
Cut into squares and serve warm or at room temperature.