Preheat your oven to 350°F and position a rack in the center. Line an 8x8-inch baking pan with foil or parchment paper, leaving an overhang on two sides to easily lift the brownies out after baking. Lightly grease the foil or parchment.

In a large mixing bowl, combine the granulated sugar and hot, melted butter. Stir gently and let the mixture sit for 5 minutes without disturbing it. During this time, the heat from the butter will begin dissolving the sugar, which contributes to a shiny, crackly crust. Note that the sugar won’t fully dissolve. After 5 minutes, whisk the butter and sugar mixture vigorously for 30 seconds. Add the eggs, water, and vanilla extract, then whisk again for another 30 seconds. Tap off any excess batter from the whisk and set it aside.

Sprinkle the cocoa powder, flour, and salt over the wet mixture. Using a rubber or silicone spatula, stir everything together until the batter is glossy and well combined.

Scoop out about one-third of the brownie batter and set it aside for creating the swirl layer. Stir the chocolate chips into the remaining batter. Pour the batter into the prepared pan and spread it evenly. Proceed to prepare the cream cheese mixture.

In a mixing bowl, use a hand mixer or a stand mixer fitted with the paddle attachment to beat the cream cheese until smooth and creamy. Add the sugar and beat until combined, followed by the flour, egg white, and vanilla extract. Beat just until fully incorporated, making sure to scrape down the sides and bottom of the bowl as needed. Avoid overbeating the mixture.

Using two spoons, drop alternating portions of the cream cheese mixture and the reserved brownie batter onto the batter in the pan. Once the dollops are in place, use the tip of a sharp knife to create swirls by moving the knife in a figure-eight or back-and-forth motion. The brownie batter will be thicker than the cream cheese mixture, so take your time to swirl them together. Focus on the surface layer and avoid swirling too deeply.

Place the pan in the preheated oven and bake for 32-37 minutes, or until the brownies are mostly set with a slight jiggle in the cheesecake areas. You can test for doneness using a toothpick—moist crumbs and melted chocolate are fine, but avoid overbaking. If the cheesecake swirls start to darken, loosely cover the pan with foil for the last few minutes of baking.

Remove the brownies from the oven and set the pan on a cooling rack. Allow the brownies to cool completely in the pan, which will take several hours. For best results, chill the brownies before slicing to achieve clean cuts and a perfect texture.