Position a rack in the center of the oven and preheat the oven to 350°F. Lightly spray an 8-inch square pan with cooking spray and line with parchment paper, leaving a 2-inch overhang on the pan's two opposite sides of the pan. Spray the parchment, too.
Make the Cheesecake Filling: In the bowl of a stand mixer fitted with the paddle attachment (or use a handheld electric mixer), combine the cream cheese, sugar, and egg. Beat on medium-high until smooth, about 1 minute. Make the Brownie Batter: Place the chocolate and butter in the top of a double boiler or in a heatproof bowl set over a medium, heavy-bottomed saucepan filled with a few inches of simmering water (be sure the bottom of the bowl does not touch the water). Cook over medium heat, using a heatproof rubber spatula to stir the mixture and scrape the sides of the bowl occasionally, until the chocolate and butter have melted and combined, about 10 minutes. Set the double boiler or bowl on a wire rack and let the chocolate mixture cool slightly, about 5 minutes.
Once the mixture cools slightly, whisk in the sugars, eggs, and vanilla one at a time, only adding the next ingredient when the previous is fully incorporated.
In a small bowl, whisk together the cornstarch, cocoa powder, and salt. Sprinkle over the wet ingredients and use the rubber spatula to mix until just combined about 1 minute.
Pour half the brownie batter into a small bowl or liquid measuring cup. If using a digital scale to divide the batter, note that this recipe makes around 25.70 ounces or 729 grams of batter; pour 12.85 ounces or 364 grams of batter into the smaller bowl/liquid measuring cup. Pour the remaining half of the brownie batter into the prepared pan and and use an offset spatula to spread it evenly across the pan. Spoon the cheesecake filling over the batter, then use the offset spatula to spread the cheesecake across the pan. Don't worry about getting it even—you'll end up swirling this layer! Finally, dollop the remaining brownie batter over the cheesecake filling. Use a butter knife to swirl the layers together. Bake for 50 to 55 minutes, or until a skewer inserted into the center of the brownies comes out with a few crumbs attached. Cool completely on a wire rack before slicing.
Run a butter knife or offset spatula along the edges of the pan and use the overhanging parchment as handles to lift the bars out of the pan and onto a cutting board. Use a hot knife to slice into 2-inch squares and serve. The brownies can be stored in an airtight container or zip-top bag at room temperature for up to 3 days.