Preheat the oven to 350°F and line an 8x8-inch baking pan with parchment paper, leaving an overhang on the sides.

In a medium microwave-safe bowl, combine the butter and chocolate. Microwave in 30-second intervals, stirring well between each spin, until the mixture is melted and smooth. (Stop heating when most of the chocolate is melted and use the residual heat to finish melting.)

Pour the chocolate and butter into a large mixing bowl. Add the granulated sugar and brown sugar and whisk until well blended. Then, whisk in the eggs and vanilla.

In a separate bowl, whisk the flour, cocoa powder, and salt. Then, slowly add the mixture to the chocolate and butter and gently stir with a rubber spatula until just combined. Do not overmix. Set aside.

In a separate bowl, beat the cream cheese until smooth. Scrape the sides and bottom of the bowl, add the sugar, and beat again until well combined. Finally, add the egg yolk and vanilla and whisk until just combined.

Pour about ¾ of the brownie batter into the prepared pan and spread evenly. Spoon the cream cheese filling over the top, then dollop the remaining brownies batter over that. Use a knife or skewer to gently swirl the batters together, then bake for 35 to 40 minutes or until a toothpick inserted into the center comes out with a few moist crumbs.

Let the brownies cool completely in the pan on a wire rack for about 2 hours. Then, use the parchment overhang to lift the brownies out of the pan and transfer to a cutting board. Slice with a sharp knife, serve, and enjoy!