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

Remove the pan from heat and let it cool to room temperature. Cover the top of the pan with plastic wrap to prevent a skin from forming.

In a stand mixer, preferably, cream together the butter and sugar on medium speed until light and fluffy, about 2-3 minutes, scraping down the sides of the bowl frequently.

Add cooled milk mixture and beat on medium speed until the frosting is light and fluffy, about 2-3 minutes.

Switch to the whisk attachment. Add vanilla and mix on high for 7-8 minutes, or until the frosting is smooth and creamy.

Spread frosting over the cooled cake.