Fluffy Vanilla Icing

This is really the best, fluffiest, most stable, buttery yet light icing I have found. I've adapted it from several similar recipes until I found my perfect fit. It makes enough to frost 24 cupcakes easily, to cover a 9x12" cake with excess, or to fill and frost a 9" cake generously.
You can vary the flavor by leaving out or substituting the vanilla extract, or adding to the finished product such things as crushed peppermint sticks, chopped nuts (in which case use 1 tsp vanilla), flaked coconut, or use your imagination.
It is best made with a stand mixer-- I used my fabulous Kitchenaid-- with the whip attachment. You will get a less fluffy result with a hand mixer, but it's still good, just increase the times necessary for beating.


Ingredients:
1 cup whole milk
5 TBS all-purpose flour
2 tsp real vanilla extract
1 cup butter, room temperature, cut into chunks
3 cups powdered sugar, loosely spooned into measuring cup
Dash salt if butter is unsalted

How to make it:
In a small saucepan, combine milk and flour with a whisk, smoothing out all lumps.
Place over medium heat and cook, constantly whisking, until mixture thickens (about 7 minutes). It should be about as thick as heavy cake batter.
Whisk in the vanilla or other flavoring at this point.
With a spatula, spread this mixture evenly onto a plate; set in a cool place (not the refrigerator) to cool down to room temperature throughout.
While it's cooling, beat butter with powdered sugar until very light, fluffy, and there is no more "gritty" feeling to it; 3-5 minutes with a Kitchenaid, longer with a hand beater.
When the flour/milk mixture is completely cooled to room temperature, add it all at once to the butter mixture and beat 2-3 minutes longer, or until very smooth and fluffy.
Use immediately to frost cooled cake layers or cupcakes.
Keep any leftover icing in a covered container in the fridge. It will get harder when cold; bring it to room temperature again to spread easily. Will keep up to a week.