Once the mixture is cool to the touch (but not hard), transfer half of the mixture to a mixing bowl with very soft butter and shortening. This is an old-style recipe, so it’s not gonna be cheap on the fats.
Whipping only half of the flour-milk mixture with the fats decreases the chances for lumps. Dumping the whole batch of the cooked flour-milk mixture into the bowl with the butter and shortening wouldn’t allow the fats to properly mix.
After a minute or so, you can add in the remaining half of the flour-milk mixture along with vanilla. The key to the light angelic texture is the aeration. Whipping the frosting for a good five to seven minutes gives it the texture you want.
