Line a square 8x8 baking dish with parchment paper hanging over all sides and preheat the oven to 350 F/180 C.
Make the cheesecake batter. Cream the sugar and cream cheese together until smooth and combined, then scrape down the sides and bottom of the bowl. Mix in the egg and vanilla until smooth. Set the bowl aside.
Add the egg and vanilla and mix until smooth and combined, about 1 ½ minutes on medium speed. Set the bowl aside.
Make the brownie batter. Melt the butter and chocolate chips together until smooth, set aside.
In a medium bowl, whisk together the eggs, vanilla, and sugar until pale and fluffy. Whisking constantly, stream the melted butter and chocolate mixture into the bowl until combined.
Fold in the flour, cocoa powder, and salt with a rubber spatula until just combined.
Scoop half of the brownie batter into the prepared baking dish, leaving some space in between each scoop. Then do the same with the cheesecake batter. Continue alternating batters, then use a toothpick or butter knife to swirl them together. Don't swirl the batters too much or you will lose the distinct marbled look!
Bake the brownies in the preheated oven for 26 minutes, or until a toothpick inserted into the center comes out covered in a few moist crumbs.
Let the brownies cool completely on a wire rack, then cut with a very hot knife into 16 servings. Store leftover brownies in an airtight container at room temperature for 3-4 days. You can also freeze them for up to 1 month!