1. Heat sugar, egg whites, and salt in a heatproof mixer bowl set over a pan of simmering water, whisking, until sugar dissolves, about 2 minutes.

2. Return bowl to mixer, and whisk, gradually increasing speed from low to medium-high, until stiff, glossy peaks form, about 10 minutes. Reduce speed to medium. Add butter, a few pieces at a time, whisking well after each addition. Whisk in vanilla. Switch to a paddle attachment. Beat until air bubbles are gone, 2 to 3 minutes more.

3. Beat in food coloring, 1 drop at a time, until desired color is achieved. (If making more than 1 color, divide buttercream and work in batches.)