In a medium saucepan, whisk together the milk and flour until smooth. Place the saucepan over medium heat and cook, whisking constantly, until the mixture thickens and resembles thick pudding. This process should take about 5-7 minutes.

Once thickened, remove the saucepan from the heat and transfer the mixture to a bowl to cool. Press a piece of plastic wrap directly onto the surface to prevent a skin from forming. Allow it to cool to room temperature.

In a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, cream together the softened butter and granulated sugar until light and fluffy, about 5 minutes. The sugar won’t completely dissolve in the butter, but the mixture should be very light in color and fluffy in texture.

Once the flour and milk mixture has cooled to room temperature, add it to the creamed butter and sugar. Beat on high speed until the frosting is light and fluffy, and resembles whipped cream. This might take about 5 minutes. Scrape down the sides of the bowl as necessary.

Mix in the vanilla extract until well combined.

The frosting is now ready to use and can be spread on cooled cakes or cupcakes. If the frosting seems too soft to spread, you can chill it in the refrigerator for about 30 minutes to firm up slightly before using.