Step 1: Prepare the Batter

1. Preheat the oven to 350°F (175°C) and line an 8×8-inch baking pan with parchment paper, leaving extra hanging over the sides for easy removal.
2. In a mixing bowl, whisk the melted butter, sugar, and brown sugar together until smooth.
3. Add eggs, vanilla extract, and red food coloring, and whisk until well combined.
4. Sift in the flour, cocoa powder, and salt. Fold the mixture gently until just combined—avoid overmixing for fudgier brownies.
5. Fold in the chopped Oreo pieces, reserving a few for the top.

Step 2: Make the Cheesecake Swirl

6. In a small bowl, beat the cream cheese, sugar, egg yolk, and vanilla until smooth.

Step 3: Assemble the Brownies

7. Pour the brownie batter into the prepared pan and spread it evenly.
8. Drop dollops of the cheesecake mixture on top of the brownie batter, then use a knife or toothpick to swirl it in gentle circular motions.
9. Sprinkle the remaining Oreo pieces on top, pressing them lightly into the batter.

Step 4: Bake

10. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs. Avoid overbaking to keep them fudgy.
11. Let the brownies cool completely in the pan before lifting them out using the parchment paper.

Step 5: Serve

12. Slice into squares and enjoy!