In a small saucepan, make a paste of the flour and a few tablespoons of the milk, stirring until smooth.
Place over low heat and add the remaining milk, cooking and stirring slowly until the mixture thickens to the consistency of a cream sauce.
Remove from heat and allow to cool to room temperature.
Put into a large mixing bowl.
In mixing bowl, cream together the butter, sugar and vanilla until smooth.
Add to the cooled milk-flour mixture.
With an electric mixer, whip the mixture until it is the consistency of whipped cream.
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