The traditional (I think) way of doing this is making a roux (boiling milk & flour until thick) then pouring over whipped butter and sugar. But for a smoother, zero grains guaranteed buttercream, you cook flour, sugar and milk, beat your butter until fluffy, then add the cooled roux a tablespoon at a time into the butter & beat. Any version would work just fine.

Pour milk, flour and sugar into a saucepan over low heat. Stir continuously to avoid clumping until a very thick consistency is attained. If you still have clumps you should strain the roux before using.

Beat butter, salt and vanilla using a hand mixer until fluffy and light.

Cool the roux.

Add one tablespoon of roux into butter, beat for a few seconds until incorporated, add another tablespoon & repeat until done.

You can add food colour.

I find that the thicker my roux is the more stable NY buttercream is (might be wrong though, I'm still experimenting.)