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1
Heat oven to 350u00b0 F. Butter the bottom but not the sides of a 9x13-inch cake pan.
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2
To make the chocolate cake batter: In the bowl of a stand mixer fitted with the paddle attachment, blend the sugar, cocoa, baking soda, butter, and eggs until smooth and well-combined.
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3
On low speed, blend the milk into the sugar mixture, scrape down the sides and bottom of the bowl with a rubber spatula, then beat on high till smooth.
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4
With the mixer on low, slowly add in the flour and salt until just combined. Blend in the boiling water, espresso powder (if using), and vanilla until well-combined, scraping down the sides and bottom to make sure it's well-mixed. The batter will be runny.
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5
Pour the batter into the prepared pan. Wash and dry the bowl and paddle (or pull out a second stand mixer bowl-they're handy!).
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6
To make the cream cheese ribbon batter: In the bowl of a stand mixer fitted with the paddle attachment, cream the butter, cream cheese, sugar, and cornstarch until light and fluffy (start on low speed then increase to medium-high once the cornstarch is all moistened).
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7
Add the eggs, milk, and vanilla and beat till smooth, scraping the sides and bottom as needed. This batter will be runny, too.
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8
Using a large spoon, gently spoon the cream cheese mixture over the chocolate cake mixture and spread it to the edges. Swirl the two batters together gently (Here's how my mom does it: Working down the 13-inch length of the cake pan, drag a table knife through the batter from edge to edge in a zigzag pattern, with zigzags spaced about 2 inches apart at the widest part.) You may not see any trace of mixing on the surface but that's okay-it will have secretly swirled underneath.
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9
Bake at 350u00b0 F until a toothpick poked in a few places comes out clean or with just crumbs clinging-start checking at 30 minutes, but it may take up to an hour to bake. It will poof in the oven, then settle as it cools. The layers swirl a little differently every time and it might look a little lumpy on top, but that's what the frosting is for.
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10
While the cake is cooling, make the frosting of your choice (see the note above for recommended recipes).
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11
Once the cake has fully cooled, frost generously in swoops. Serve squares directly from the pan with glasses of cold milk.
