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 the bowl to the mixer fitted with the whisk attachment. Starting on low and gradually increasing to medium-high speed, whisk until stiff (but not dry) peaks form. Continue mixing until the mixture is fluffy and glossy, and completely cool (test by touching the bottom of the bowl), about 10 minutes.

With the mixer on medium-low speed, add the butter, a few tablespoons at a time, mixing well after each addition. Once all butter has been added, whisk in vanilla.

Switch to the 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 the frosting is completely smooth.

Before tinting buttercream, reserve some for toning down the color, if necessary. To the remaining buttercream, add gel-paste food coloring, a drop at a time (or use a toothpick or skewer to add food color a dab at a time). You can use a single shade of food coloring or experiment by mixing two or more.

Blend after each addition with the mixer (use a paddle attachment) or a flexible spatula, until desired shade is achieved. Avoid adding too much food coloring too soon, as the hue will intensify with continued stirring; if necessary, you can tone down the shade by mixing in some reserved untinted buttercream.