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Preheat the oven to 350F (175C).
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Line the inside of a 9-inch (23-cm) 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.
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Or, use one large sheet of extrawide foil.
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Lightly grease the foil with butter or nonstick cooking spray.
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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.
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Remove from the heat and stir in the 2/3 cup (130 g) sugar followed by the 2 eggs.
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Mix in the flour, cocoa powder, and salt, then stir in the 1 teaspoon vanilla and the chocolate chips.
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Scrape the batter into the prepared pan and spread evenly.
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To make the cheesecake topping, in a medium bowl, beat together the cream cheese, egg yolk, the 5 tablespoons (75 g) sugar, and 1/8 teaspoon vanilla until smooth.
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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.
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Resist the urge to mix and swirl too much, as youll just make the brownies muddyyou want big pockets of cheesecake.
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Bake until the brownies feel just set in the center, about 35 minutes.
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Let cool completely in the pan before lifting out the foil to remove the brownies.
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The brownies will keep in an airtight container for 2 days.
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They can also be frozen, wrapped well, for 1 month.
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(And in fact, if you cut them and store them individually wrapped, theyre terrificand convenientto eat while frozen.
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See Tip, page 196, for brownie-cutting techniques.)
