Combine egg whites, sugar, and salt in the heatproof bowl of a standing mixer set over a pan of simmering water. Whisk constantly by hand until mixture is warm to the touch and sugar has dissolved (the mixture should feel completely smooth when rubbed between your fingertips).
Attach bowl to mixer fitted with whisk attachment. Starting on low and gradually increasing to medium-high speed, whisk until stiff (but not dry) peaks form. Continue mixing until mixture is fluffy and glossy, and completely cool (test by touching bottom of bowl), about 10 minutes.
With mixer on medium-low speed, add butter a few tablespoons at a time, mixing well after each addition. Once all butter has been added, whisk in vanilla. Switch to paddle attachment, and continue beating on low speed until all air bubbles are eliminated, about 2 minutes. Scrape down sides of bowl with a flexible spatula, and continue beating until frosting is completely smooth.
Beat in completed Vanilla Creme Anglaise. Keep buttercream at room temperature if using the same day.