Preheat oven to 350 degrees F. Grease the bottom and sides of a 9-inch by 9-inch baking pan.
Make the brownies: In a large bowl, combine cake mix, milk, oil and egg. Fold in chocolate pieces and spread in an even layer onto the baking pan.
Make the cheesecake swirl: In the bowl of a stand mixer (or in a medium bowl and using a hand mixer), add cream cheese, remaining egg and sugar. Beat until combined and smooth, about 1 minute. Spoon dollops of cream cheese mixture on top of brownies. Use a butter knife to gently drag the cream cheese through the batter, creating a marbled effect.
Bake brownies for 25-27 minutes, or until a toothpick inserted into the center of the dish comes out with just a few crumbs. (Not gooey, unless it hits a chocolate chip.)
