Preheat oven to 350°F (175°C). Grease a 9x13-inch baking pan.
In a medium bowl, combine the cake mix, 2 eggs, melted butter, flour, and a pinch of salt. Mix until just combined, then press evenly into the bottom of the prepared pan. Set aside.
In a large bowl, beat the cream cheese, sugar, remaining egg, vanilla, and salt until smooth and fluffy.
Pour the cream cheese mixture over the cake base in the pan, spreading it evenly.
Bake for 40–45 minutes, or until the top is lightly golden and the center is set but still slightly soft.
Cool completely on a wire rack before slicing and serving.
Notes
Serve warm or at room temperature for best flavor.