1. In a 4-quart stainless pot, combine the milk, vanilla, and half of the sugar. Scald over a medium heat. Set it aside.
2. In a standing 5-quart electric mixer with the wire whisk attachment, beat the egg yolks and remaining sugar until they turn a pale yellow colour and a thick ribbon forms from the beater.
3. With the mixer running at a medium speed, pour in a third of the milk. When incorporated, whisk the egg mixture back in the pot with the remaining milk. Boil over high heat. Whisk constantly.
4. Remove the mixture from the heat and strain through a fine mesh strainer back into the mixing bowl. With the mixer running on medium speed, beat it until the mixture doubles in volume. Set it aside.
5. In another mixing bowl (or the same one, if you clean out the contents and wash it thoroughly) beat the butter (with the paddle attachment) 3 to 5 minutes until it whitens in colour. With the mixer running, pour the egg/milk mixture in a steady fashion down the sides of the bowl. Continue beating the cream on a meduim speed until the lower part of the bowl is cool, and the buttercream is shiny and silky. The buttercream might separate, but you can keep beating and it will come back together.
DO NOT ATTEMPT TO MAKE BUTTERCREAM UNDER VERY HOT CONDITIONS, BECAUSE IT WILL SEPARATE AND NOT COME TOGETHER EVEN WITH CONTINUAL BEATING.
Note: The buttercream frosting is usually for wedding cakes, and can be made up to 1 week ahead and kept in the refregerator. Also, it can be frozen for up to 2 monthes, let the cream defrose, then re-beat before using.