Preheat the oven to 350°F (175°C). Line the inside of an 8-inch (20-centimeter) square pan with 2 lengths of foil, positioning the sheets perpendicular to each other and allowing the excess to extend beyond the edges of the pan. Lightly grease the foil with butter or nonstick cooking spray.

To make the brownies, in a medium saucepan, melt the butter, then add the chopped bittersweet or semisweet chocolate and stir over low heat until the chocolate is melted and smooth. Remove from the heat and stir in the ⅔ cup (130 grams) sugar followed by the 2 eggs. Mix in the flour, cocoa powder, and salt, then stir in the 1 teaspoon vanilla and the chocolate chips. Scrape the batter into the prepared pan and spread evenly.

To make the cheesecake topping, in a medium bowl, beat together the cream cheese, egg yolk, the 5 tablespoons (75 grams) sugar, and ⅛ teaspoon vanilla until smooth. Distribute the cream cheese mixture in 8 dollops across the top of the brownie batter, then, with a butter knife or spatula, swirl the cream cheese mixture very slightly into the batter. Resist the urge to mix and swirl too much, as you’ll just make the brownies muddy—you want big pockets of cheesecake.

Bake until the brownies feel just set in the center, about 35 minutes. Let cool completely in the pan before lifting out the foil to remove the brownies.

The brownies will keep in an airtight container for 2 days. They can also be frozen, wrapped well, for at least 1 month.