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Preheat the oven to 350°F. Line a 9" x 13" pan with a parchment paper sling then lightly grease the parchment and exposed sides of the pan.
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To make the brownie batter: In a large saucepan, melt the butter, then stir in the sugar, cooking until the mixture is smooth and shiny.
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Remove from the heat and stir in the cocoa, salt, baking powder, espresso powder, and vanilla. Allow to cool slightly, around 5 minutes.
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Whisk in the eggs, then the flour, stirring until smooth.
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To make the cream cheese batter: Beat the cream cheese until no lumps remain. Mix in the sugar and flour, then the vanilla, cream, and eggs.
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Fold the chocolate chips into the brownie batter.
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To assemble the cheesecake brownies: Spoon half the brownie batter into the prepared pan, then top with the cream cheese batter.
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Dollop the remaining brownie batter onto the cream cheese, swirling the two together.
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Bake the cheesecake brownies for 40 to 45 minutes, until a tester inserted into the center comes out clean, and the edges are set.
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Remove the cheesecake brownies from the oven, and loosen the edges with a table knife. Cool completely (preferably overnight) before cutting.
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Storage information: Store leftover cheesecake brownies, well-wrapped, in the refrigerator for several days. Freeze for longer storage.