In a medium saucepan, whisk together the flour and milk until smooth.

Place the saucepan over medium heat and continue to whisk constantly until it thickens and bubbles, about 5-10 minutes.

Remove the saucepan from heat and allow the mixture to cool to room temperature.

In a mixing bowl, beat the butter and sugar together until light and fluffy, about 3-5 minutes.

Gradually add the cooled flour mixture to the butter mixture while beating on medium speed.

Mix in the vanilla extract and beat until fully incorporated.

If the icing is too thick, add a tablespoon of milk to loosen it.

Use the icing immediately to frost your cakes or cupcakes.