In a saucepan, whisk together the sugar, flour, and salt. While whisking, add in the milk, cream, and then the egg yolks.

Bring to a simmer over medium-low heat, whisking almost constantly, paying attention that no build-up happens along the bottom edges of the pan. Continue to simmer gently for several minutes until a finger leaves a clear distinct line when run across the back of a spoon that has been dipped in the mixture.

Remove from heat, and while continuing to whisk, add the butter and the vanilla. For the smoothest sauce, push through a strainer.

Serve warm or chilled.