Line a 9-inch (23cm) or 8-inch (20cm) square pan with foil, making sure it goes up all four sides. Use two sheets if necessary. Mist with non-stick spray or grease lightly.
Preheat oven to 350 degrees (180C).
In a medium saucepan, to make the brownie batter, melt the butter and chocolate over low heat, stirring until smooth. Remove from heat and beat in the 2/3 cup (130g) sugar, then the eggs.
Mix in the flour, cocoa powder and salt, then the vanilla and chocolate chips. Spread evenly in the prepared pan.
In a separate bowl for the cheesecake topping, beat together the cream cheese, the yolk, 5 tablespoons (75g) of sugar, and vanilla until smooth.
Distribute the cream cheese mixture in eight dollops across the top of the brownie mixture, then take a dull knife or spatula and swirl the cream cheese mixture with the chocolate batter. Rap the pan on a countertop a few times to let the batter and swirl settle together.
Bake until the batter in the center of the pan feels just set, 35 to 40 minutes.
Let cool, then lift the brownies out holding the foil and peel it away. Cut the brownies into squares.
