Step 1

In a medium saucepan over medium heat, whisk together the milk and flour. Cook, whisking constantly, for 3-5 minutes, or until no lumps remain and the mixture thickens and resembles a very thick pudding. It should coat the back of a spoon.

Step 2

Remove the pan from the heat and let the mixture cool to room temperature. (The mixture will get lumpy again as it cools.)

Step 3

In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter, sugar, and cocoa powder on low speed until the cocoa powder is incorporated. Increase the speed to medium and mix until light and fluffy (2-3 minutes). Stop the mixer and use a rubber spatula to scrape down the sides of the bowl as needed.

Step 4

Add the cooled milk mixture to the bowl of the stand mixer. Beat on medium-high speed until the frosting is light and fluffy (2-3 minutes), pausing to scrape down the sides of the bowl as needed.

Step 5

Switch to the whisk attachment. Add vanilla and mix on high for 8-10 minutes, or until the frosting is smooth and creamy.