In a saucepan, whisk the milk and flour together until smooth. Bring this mixture to a boil and stir constantly until it turns into a thick, roux-like paste.
Remove the saucepan from the heat and stir in the sugar to dissolve it. Let the mixture cool to about 70°F.
Leave the butter out on the counter or use short bursts in the microwave to make it soft and pliable but still cool.
Use the paddle attachment of a mixer to beat the butter until it's creamy, light, and holds its shape.
Gradually add and beat the cooled milk paste to the butter. Once everything is combined and smooth, whip with the mixer until the frosting is airy and light.