Step 1
For the Cake: Adjust oven rack to middle position and preheat to 350°F (175°C). Grease a 10- by 15-inch rimmed baking sheet or 9- by 13-inch baking pan with butter and dust with cocoa powder, shaking out excess. (See notes.)
Step 2
In a small saucepan, bring beer to a simmer over medium heat; remove from heat and set aside. Meanwhile, in a large bowl, whisk flour, sugar, cocoa powder, baking powder, baking soda, and salt together to combine.
Step 3
Add eggs, milk, oil, and vanilla to flour mixture; whisk until well combined and no streaks remain. Gradually pour warmed beer into batter and whisk to combine. (Batter will be thin.) Pour batter into prepared pan.
Step 4
Bake until a toothpick or cake tester inserted into the center comes out clean and cake springs back when gently touched, 25 to 30 minutes. Remove from oven and cool completely in pan on a wire rack, about 1 hour.
Step 5
While the cake cools, prepare the Guinness Syrup : In a small saucepan, whisk beer, sugar, and espresso granules to combine. Bring to a simmer over medium heat; cook, stirring often, until sugar is dissolved, about 2 minutes. Remove from heat.
Step 6
Using a fork, poke the cooled cake all over. Using a pastry brush, brush cake with syrup until all the liquid is absorbed. (It may look like a lot of liquid, but the cake will soak it all up.)
Step 7
For the Malted Vanilla Frosting: In the bowl of a stand mixer fitted with the paddle attachment, beat cream cheese, sugar, malted milk powder, vanilla, and salt on medium speed until smooth, using a flexible spatula to scrape down bowl and beater as needed, about 1 minute. Increase the speed to high, then gradually add heavy cream until mixture is smooth and medium-stiff peaks form, 5 to 6 minutes. (Alternatively, frosting can be prepared in a large bowl with an electric hand mixer.)
Step 8
Using a flexible spatula or offset spatula, spread frosting over cooled cake. Refrigerate until chilled and set, about 1 hour.