Whisk egg whites and sugar in a heatproof mixer bowl set over a pan of simmering water. Whisk until sugar dissolves and mixture is warm. Attach to mixer, and whisk on high speed until thick and cooled, about 10 minutes. Reduce speed to medium-low. Add butter, a few pieces at a time, beating well after each addition. Beat in food coloring a drop at a time. Reduce speed to low and beat until smooth.