Chocolate-Mocha Espresso Cake

Step 1: Heat the oven to 350°F and arrange a rack in the middle. Coat a 13-by-9-inch glass baking dish with butter and flour; set aside.

Step 2: FOR THE CAKE: Whisk together the measured flour, baking soda, and salt in a medium bowl; set aside.

Step 3: Whisk together the cocoa, boiling water, and espresso powder in a small bowl until combined. Slowly whisk in the milk; set aside.

Step 4: 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. Add the sugar and vanilla and continue to beat for another 4 minutes. Stop the mixer and scrape down the sides of the bowl and the paddle with a rubber spatula.

Step 5: Return the mixer to medium-high speed. Add the eggs 1 at a time, letting each incorporate fully before adding the next. Stop the mixer and scrape down the sides of the bowl and the paddle again.

Step 6: Add a third of the flour mixture and turn the mixer to low speed, mixing until the flour is just incorporated. Add half of the cocoa mixture and mix until just incorporated. 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. Stop the mixer, remove the bowl, and stir in any remaining flour streaks by hand, making sure to scrape the bottom of the bowl.

Step 7: Pour the batter into the prepared dish and spread it into an even layer. Bake for 15 minutes, then rotate the dish. 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 15-20 minutes more. Transfer to a wire rack to cool completely before frosting, at least 2 hours.

Step 8: FOR THE FROSTING: Fill a medium saucepan with 2 inches of water and bring it to a boil over high heat. Place the espresso powder in a small bowl, add 1 teaspoon of the boiling water, and stir until the powder has dissolved; set aside.

Step 9: Reduce the heat to low so the water is just simmering. Place the milk and bittersweet chocolates in a heatproof bowl large enough to sit over the water without touching it. Place the bowl over the saucepan and stir until the chocolate is melted and smooth. Set aside until cooled slightly but still pourable, about 5 to 10 minutes.

Step 10: 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.

Step 11: Add the dissolved espresso powder and beat until incorporated. Pour in the chocolate and mix until completely incorporated. Add the vanilla and salt and mix until incorporated. Stop the mixer and scrape down the sides of the bowl and the paddle with a rubber spatula.

Step 12: Turn the mixer to low and slowly add the powdered sugar until it’s incorporated and the mixture is creamy, about 1 1/2 minutes. Increase the speed to high and mix until lightened in color and fluffy, about 1 minute more.

Step 13: Spread all of the frosting in an even layer over the cooled cake. If you don’t plan to eat the cake within 4 hours, cover it with plastic wrap and refrigerate for up to 3 days. Before serving, let the cake sit at room temperature for about 45 minutes to take the chill off.