Preheat oven to 350°F. Grease a 9×9-inch baking dish and set aside.
Prepare the brownie mix according to package directions (there are slight differences in the amount of oil and water used, depending on which brownie mix is being used). Reserve 1 cup of batter and set to the side. Pour remaining batter into baking pan.
Prepare cheesecake filling. Add peppermint candies to the bowl of a food processor and mix on high until candies are very finely ground. Add remaining cheesecake filling ingredients to the food processor and mix until smooth.
Use a spoon to dollop heaping tablespoons of cheesecake filling across the brownie batter. Scoop the reserved brownie batter on top of the cheesecake filling (it will not fully cover the cheesecake filling). Use a knife to swirl the cheesecake filling into the brownie batter, working from side to side (left-to-right and top-to-bottom)
Bake 35-40 minutes. Allow to completely cool before cutting. Store covered in the refrigerator.