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1
Heat the oven to 350 degrees F and arrange a rack in the middle.
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2
Coat a 13-by-9-inch glass baking dish with butter and flour; set aside.
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3
Whisk together the measured flour, baking soda, and salt in a medium bowl; set aside.
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4
Whisk together the cocoa, boiling water, and espresso powder in a small bowl until combined.
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5
Slowly whisk in the milk; set aside.
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6
Place the measured butter in the bowl of a stand mixer fitted with a paddle attachment and beat on medium-high speed until fluffy and light in color, about 3 minutes.
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7
Add the sugar and vanilla and continue to beat for another 4 minutes.
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8
Stop the mixer and scrape down the sides of the bowl and the paddle with a rubber spatula.
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9
Return the mixer to medium-high speed.
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10
Add the eggs 1 at a time, letting each incorporate fully before adding the next.
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11
Stop the mixer and scrape down the sides of the bowl and the paddle again.
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12
Add a third of the flour mixture and turn the mixer to low speed, mixing until the flour is just incorporated.
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13
Add half of the cocoa mixture and mix until just incorporated.
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14
Continue adding the remaining flour mixture and cocoa mixture, alternating between each and ending with the flour, until all of the ingredients are incorporated and smooth.
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15
Stop the mixer, remove the bowl, and stir in any remaining flour streaks by hand, making sure to scrape the bottom of the bowl.
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16
Pour the batter into the prepared dish and spread it into an even layer.
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17
Bake for 15 minutes, then rotate the dish.
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18
Continue baking until the cake edges slightly pull away from the dish and a cake tester or toothpick inserted into the center comes out dry with just a few crumbs, about 15 to 20 minutes more.
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19
Transfer to a wire rack to cool completely before frosting, at least 2 hours.
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20
Fill a medium saucepan with 2 inches of water and bring it to a boil over high heat.
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21
Place the espresso powder in a small bowl, add 1 teaspoon of the boiling water, and stir until the powder has dissolved; set aside.
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22
Reduce the heat to low so the water is just simmering.
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23
Place the milk and bittersweet chocolates in a heatproof bowl large enough to sit over the water without touching it.
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24
Place the bowl over the saucepan and stir until the chocolate is melted and smooth.
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25
Set aside until cooled slightly but still pourable, about 5 to 10 minutes.
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26
Beat the butter in the bowl of a stand mixer fitted with a paddle attachment on medium-high speed until light and fluffy, about 3 minutes.
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27
Add the dissolved espresso powder and beat until incorporated.
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28
Pour in the chocolate and mix until completely incorporated.
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29
Add the vanilla and salt and mix until incorporated.
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30
Stop the mixer and scrape down the sides of the bowl and the paddle with a rubber spatula.
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31
Turn the mixer to low and slowly add the powdered sugar until its incorporated and the mixture is creamy, about 1 1/2 minutes.
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32
Increase the speed to high and mix until lightened in color and fluffy, about 1 minute more.
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33
Spread all of the frosting in an even layer over the cooled cake.
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34
If you dont plan to eat the cake within 4 hours, cover it with plastic wrap and refrigerate for up to 3 days.
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35
Before serving, let the cake sit at room temperature for about 45 minutes to take the chill off.
