Heat oven to 350°F. Line an 8-inch square pan with parchment, leaving overhang. Lightly grease.
Beat cream cheese with sugar until smooth. Mix in egg yolk, vanilla, and flour. Set aside.
Whisk melted butter and sugar in a bowl until glossy and combined.
Add eggs and vanilla. Whisk until the batter looks thick and shiny.
Sift in flour, cocoa, and salt. Fold just until no dry streaks remain.
Stir in chocolate chips, if using.
Spread about two-thirds of the brownie batter into the pan.
Dollop spoonfuls of cream cheese mixture over the batter. Spoon on remaining brownie batter.
Swirl gently with a knife or skewer, creating ribbons without overmixing.
Bake 32–36 minutes, until a toothpick has a few moist crumbs. Cool completely in pan.
Chill 30–60 minutes for cleaner cuts. Lift out and slice into 16 squares.