Preheat the oven to 350°F (175°C) and line a 9×9-inch baking dish with parchment paper.
In a saucepan over medium heat, melt the butter and continue cooking until lightly browned and fragrant.
Remove from heat and stir in the chocolate chips until fully melted and smooth. Let cool slightly.
In a large bowl, whisk together the granulated sugar, brown sugar, salt, and eggs for 2–3 minutes until thick, pale, and glossy.
Whisk in the vanilla extract and espresso powder until fully combined.
Slowly pour the chocolate mixture into the egg mixture while whisking continuously until smooth and glossy.
Sift in the cocoa powder and flour, then fold gently until just combined. Do not overmix.
In a separate bowl, beat together the cream cheese, mascarpone, sugar, egg, and vanilla until smooth and creamy.
Pour most of the brownie batter into the prepared pan, reserving about ½ cup.
Spoon the mascarpone cream mixture over the brownie batter.
Dollop the remaining brownie batter on top.
Use a knife or skewer to gently swirl the layers together, creating a marbled pattern. Do not over-swirl.
Bake for 40–45 minutes, until the edges are set and the center has a slight jiggle.
Allow to cool completely before slicing.