Heat oven to 350°F. Line an 8-inch square pan with parchment, leaving overhang.
Whisk melted butter, granulated sugar, and brown sugar in a bowl until glossy.
Beat in eggs and vanilla until mixture is thick and shiny, about 30 seconds.
In another bowl, whisk flour, cocoa, salt, and espresso powder to combine.
Fold dry ingredients into the wet just until no flour streaks remain.
Stir in chocolate chips, reserving a small handful for topping.
Spread about two-thirds of the brownie batter into the prepared pan.
Beat cream cheese and 1/3 cup sugar until smooth. Mix in sour cream, egg, and vanilla.
Dollop cheesecake mixture over brownie layer. Spoon remaining brownie batter in small mounds.
Swirl gently with a knife. Sprinkle reserved chocolate chips on top.
Bake 32–38 minutes, until edges are set and center has a slight wobble.
Cool completely in the pan. Chill 30 minutes for cleaner slices, then cut into squares.