Preheat the oven to 350-degrees F. Prepare an 8×8 baking pan with nonstick cooking spray or coconut oil; set aside.
For the brownie batter, in a large bowl, beat the eggs in an electric mixer fitted with a paddle attachments.
Add in the butter, sugar, vanilla extract, flour, cocoa powder, salt, food coloring and vinegar. Mix until well combined.
Transfer the mixture into the prepared pan.
To make the cheesecake swirl, beat the cream cheese until smooth. Blend in the sugar, egg yolk, and vanilla extract until smooth.
Drop the cream cheese mixture by tablespoonfuls onto the brownie mixture. Use a knife to swirl the cream cheese mixture into the brownie batter. Sprinkle the chocolate chips over the top.
Bake for 28-30 minutes until a tester inserted into the center comes out clean. Cool completely before cutting.
Store leftovers in the refrigerator for a week.