Preheat the oven to 325°F. Line an 8x8 square baking dish with parchment paper and set it aside.
Mix up brownie mix according to package instructions. Reserve ½ cup brownie mix and pour the remaining batter into the prepared baking dish.
Beat together cream cheese, sugar, and vanilla extract until smooth.
Beat in egg gently.
Drop scoops of cream cheese mixture onto the brownie batter.
Mix a tablespoon of water into the reserved brownie batter to thin it out just a bit. Drop this remaining brownie batter over the top of the batter in the baking dish, between the scoops of cream cheese mixture.
Use a knife or spatula to gently swirl the cream cheese mixture and brownie batter.
Bake until a toothpick inserted into the brownies comes out with just a few crumbs on it (approximately 50 to 55 minutes).
Allow brownies to cool completely before cutting into them.