Preheat oven to 350 degrees F. Spray an 8x8-inch pan with nonstick cooking spray or line pan with aluminum foil.

Combine brownie mix, eggs, and butter in a large mixing bowl. Stir until smooth. You can do this with a wooden spoon or electric mixer.

Reserve a 1/2 cup of batter. Spread remaining batter into the prepared pan.

Combine cream cheese and granulated sugar in a medium bowl. Beat until smooth. Use a handheld mixer for this. Be sure to use room temperature cream cheese or your batter will be lumpy. Add the egg and vanilla extract. Stir until batter is smooth.

Spread cream cheese mixture evenly over the brownie batter. Drop the remaining 1/2 cup of brownie batter evenly over the cheesecake topping. Swirl batters together with a knife of offset spatula.

Bake until golden brown, about 35 minutes.

Allow brownies to cool for several hours. Cut into squares and serve. Store, wrapped, on the counter for up to three days.