Use this to make our Mother-Hen Cake.
Put butter in the bowl of an electric mixer fitted with the whisk attachment. Beat until pale and fluffy, about 3 minutes. Transfer to another bowl.
Whisk together sugar and egg whites in a heatproof mixing bowl set over a pan of simmering water. Whisk gently until sugar is dissolved, about 3 minutes.
Transfer sugar mixture to the clean bowl of an electric mixer. Beat on medium speed until fluffy and cooled, about 10 minutes. Raise speed to high; beat until stiff peaks form. Reduce speed to medium- low; add butter, 2 to 3 tablespoons at a time. Mix in vanilla. Reduce speed to low; beat 3 minutes more.
Tint 2 cups buttercream burnt-red-orange using red, orange, and brown food coloring. Tint 1/2 cup buttercream yellow-orange using yellow and orange. Leave remaining buttercream white.