Preheat the oven to 350 °F (175 °C) and line an 8×8 pan with parchment or foil, leaving an overhang for easy lifting.
Melt the chocolate chips and butter together using a double boiler or gentle heat. Whisk in the cocoa powder, then stir in both sugars. After it cools slightly, whisk in eggs, vanilla, and salt. Fold in the flour just until combined.
Beat the softened cream cheese and sugar until creamy. Add the egg and vanilla and mix until smooth.
Pour most of the brownie batter into the pan. Spread the cream cheese mixture on top in dollops and add the remaining brownie batter in small spoonfuls. Swirl gently with a knife or toothpick.
Bake for 30–40 minutes, or until the center is just set and a toothpick comes out with a few moist crumbs. Cool completely before slicing.