In a medium-sized bowl, beat 8 oz. or 1 cup of room temperature cream cheese on a medium-high speed with a hand mixer or stand mixer fitted with a whisk attachment for a minute until it's creamy and smooth.
Gradually mix in 2/3 cup of sugar and 1 tsp of vanilla. Mix on a medium-low speed until incorporated.
Then mix in 1 egg at medium-low speed until combined. Scrape the sides and bottom of the bowl as needed with a rubber spatula. At this stage, the cheesecake batter should look silky smooth.
Fold in 1/2 cup of roughly chopped Oreos. Mix until they're evenly distributed throughout the batter.
Alternate spoonfuls of brownie batter and cheesecake filling on top of the cooled Oreo crust. Use a butter knife or small offset spatula to swirl the batter together.
Bake at 350°F/175C° for 40-45 minutes or until the edges of the brownies look set. The toothpick test won't work with these because of the cheesecake swirl, so I like to do a jiggle test. The edges should be set, but the center can still be a little wiggly once they're done. In my oven, the sweet spot is 44 minutes, but every oven bakes a bit differently! If you notice the cheesecake swirl is browning towards the end of the baking process, place a piece of foil over the pan.
Remove the pan from the oven and cool fully before cutting. You can accelerate the cooling process by popping the pan in the freezer for about an hour. I like these best when they're chilled and straight out of the fridge!