Preheat oven to 350°F with a rack in the center of the oven. Line an 8×8* pan with foil or parchment paper, leaving a couple inches of overhang on two sides (this will allow you to lift the whole tray of brownies out of the pan for easy removal). Grease the foil/parchment.

Combine granulated sugar and hot butter in a large bowl. Stir it briefly then allow it to sit undisturbed for 5 minutes. The heat from the butter will begin to dissolve the sugar (this helps make a shiny/crackly crust), the sugar will not fully dissolve. After 5 minutes, whisk the butter and sugar vigorously for 30 seconds. Add eggs, water, and vanilla extract, whisking again for about 30 seconds. Tap all the excess batter off the whisk and remove the whisk from the bowl.

Sprinkle cocoa powder, flour, and salt over the wet ingredients. Use a rubber/silicone spatula to stir the mixture until it is glossy and well combined.

Scoop out about one third of the brownie mixture and set it aside for the swirl layer. Stir the chocolate chips into the remaining brownie batter. Add the batter to the prepared pan and spread into an even layer. Prepare the cream cheese mixture.

Using a hand mixer or stand mixer with the paddle attachment, beat cream cheese until smooth. Beat in sugar, followed by flour, egg white, and vanilla. Beat until combined, scraping the sides and bottom of the bowl as necessary. Be careful not to overbeat.

Using two tablespoons, alternate dropping portions of cream cheese and portions of the reserved brownie batter all over the top of the batter that is in the pan. Use the tip of a sharp knife to swirl the batter together. The brownie batter will be thicker than the cream cheese batter, just take your time moving in a figure 8 or back and forth motion and they will swirl together. Don’t swirl too deep; you are mostly just making visible swirls in the top layer of brownie and cream cheese.

Bake for 32-37 minutes until it is mostly set but there is still a slight jiggle in the cheesecake areas. You can check doneness with a toothpick; moist fudgy crumbs and melted chocolate are OK. Be careful not to over bake. If you notice your cheesecake swirls darkening you can loosely cover the baking dish with foil for the last 5 minutes or so. Remove from the oven and place on a cooling rack to cool completely (this will take several hours).