Preheat your oven to 350 degrees F. Coat an 8-inch x 8-inch square pan with non-stick cooking spray. (see note)
Prepare the brownie batter according to the package directions. Reserve 4 tablespoons of brownie batter in a small bowl and then pour the rest into the prepared pan.
In a medium mixing bowl, beat together the cream cheese, powdered sugar, and vanilla until smooth.
Beat the egg into the cream cheese mixture and once combined, pour the cheesecake batter over the brownie batter. Spread the cheesecake into an even layer.
Stir the milk into the reserved brownie batter until combined. Place dollops of the thinned batter over the cheesecake. Then use a knife or skewer to swirl the dollops into the cheesecake.
Bake for 30-35 minutes or until the cheesecake is firm and a toothpick inserted in the center comes out clean.
Turn off the oven and leave the pan inside for 30 minutes. then remove the brownies and let them cool in the pan on a wire rack until they reach room temperature.
Transfer to cooled brownies to the fridge to chill for at least 1 hour before cutting into 12 pieces and serving.
Notes
I recommend lining the pan with parchment paper, letting is hang over the edge, and spraying again. This makes it SUPER easy to take the brownies out of the pan.