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1
Put the flour and sugar into a medium saucepan. Stir with a whisk until combined. Slowly add the cold milk, whisking all the while, until all the milk is added and there are no lumps.
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2
Put the pan on medium heat and cook, stirring frequently, until the mixture thickens and comes to a boil. Once it starts simmering, you'll need to stir constantly to keep it from burning. The mixture will be *very* thick, almost like library paste.
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3
Once it comes to a boil, turn the heat to low and cook for another three minutes, stirring constantly, to cook out any raw flour taste. This is the frosting base.
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4
Take the frosting base off the heat and put a piece of plastic wrap over the surface to prevent a skin from forming. Set the frosting base aside to cool to room temperature (you can speed this along by skipping the plastic wrap and whisking the frosting base over a bowl of ice water).
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5
About 20 minutes before you're ready to finish the frosting, take the butter out of the fridge. You want it to be cool but malleable when you add it to the frosting base, which may take more or less time depending on how hot your kitchen is.
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6
Cut the butter into small pieces, about 1/4 tablespoon each.
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7
Put the frosting base into the bowl of a stand mixer with the whisk attachment and add the vanilla and salt. Turn the mixer to medium and beat until the extract and salt are fully incorporated, about 30 seconds. Turn off the mixer and scrape down the sides of the bowl.
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8
Turn the mixer back on and add the butter, one piece at a time. Wait until one piece is fully incorporated before adding the next. The frosting may go through a stage where it looks broken and curdled. Don't worry--keep beating. This just means that the butter is too cold to incorporate smoothly into the frosting base base at the moment. More beating will fix that.
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9
Once you have added all of the butter, turn the mixer to high and beat for 5-7 minutes, until the frosting is ethereally light and fluffy.
