Whisk together the flour and the milk. Heat in a small sauce pan on medium heat.

Whisk continuously until it starts to thicken. Let it cook, while stirring with a rubber spatula, until you can start to see the bottom of the pan. Continue to cook until mixture has the consistency of thick pudding or paste.

Put  mixture in the fridge and let it cool completely; it's fine if it stays in there long enough to get chilly, you just don't want it warm at all. As it's cooling, feel free to stir it occasionally to speed up the process and keep it from forming a crust on top. You can also do this quickly in the freezer, just keep an eye on it so it doesn't freeze.

Using the whisk attachment on an electric stand mixer, beat the butter and the sugar for a minute or two until well combined and fluffy. While beating, add in the thickened milk mixture and the flavor extracts. Beat to combine and then scrape down the sides. Mixture will separate and look messy, keep beating!  Continue beating until mixture comes together and is light and fluffy, about 7-8 minutes, but time varies.  Take a sample of frosting between your fingers; frosting is done when light and fluffy and sugar granules are dissolved.