Whisk together flour, sugar and salt in a saucepan.

Add the milk and whisk until combined

Place saucepan over low heat and whisk constinouosly as the mixture comes to a boil

Once it boils , cook for 1-2 minutes, then take the pan off the heat and whisk for a minute or so. It should be lump free and smooth

Transfer the pudding into another bowl or plate . Cover it with plastic wrap, pressing the plastic wrap directly onto the pudding. This prevents a skin from forming. Let the pudding to cool to room temperature

Once the pudding is cool, beat the butter until fluffy and pale,.This will take 5-10 minutes using an electric mixer and much longer using a wooden spoon or whisk ( but doable).

Once the butter is really smooth and pale (important!) , add the cooled pudding one tablespoon at a time, mixing or beating well after each addition

After all the pudding has been added, mix or beat for another 3-5 minutes. The buttercream should be smooth and creamy

Beat in the vanilla or other flavouring . Your buttercream is ready !