Preheat oven to 350°F (175°C). Grease and flour a 9x9 inch baking pan.
In a medium bowl, whisk together melted butter and sugar. Beat in eggs one at a time, then stir in vanilla extract.
In a separate small bowl, whisk together flour, cocoa powder, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Stir in chocolate chips.
In another bowl, beat cream cheese and sugar until smooth. Beat in egg yolk and vanilla extract until well combined.
Spread half of the brownie batter into the prepared pan. Dollop the cheesecake mixture over the brownie batter and swirl gently with a knife or skewer.
Spoon the remaining brownie batter over the cheesecake layer and swirl again gently.
Bake for 30-35 minutes, or until a toothpick inserted into the center comes out with moist crumbs (not wet batter).
Let cool completely in the pan before cutting into squares.
Notes
For an extra rich flavor, you can add a pinch of espresso powder to the brownie batter. Ensure cream cheese is at room temperature for a smooth cheesecake swirl.