Heat sugar and eggs: Bring a saucepan filled with about 2 inches of water to a simmer. Meanwhile, combine sugar, egg whites, and salt in a large heat-proof mixing bowl. Set bowl over (not in) simmering water, and whisk until whites are warm to the touch and sugar is dissolved, 2 to 3 minutes. (Heating the eggs relaxes their proteins, enabling the eggs to whip up higher and more quickly; the sugar also melts, for a silky smooth consistency.) Test by rubbing between your fingers; the mixture should feel smooth.
Whip meringue: Attach bowl to a standing electric mixer fitted with the whisk attachment, and beat on low speed until foamy. Add cream of tartar, and beat on medium-high speed until stiff, glossy peaks form and mixture is cooled completely, about 10 minutes.
Mix in butter: Reduce speed to medium-low; add butter 2 tablespoons at a time, beating to incorporate fully after each addition. Don't worry if the buttercream appears curdled at this point; it will become perfectly smooth again with continued beating. After all the butter has been incorporated, beat in vanilla.
Finish: Switch to the paddle attachment. Beat on the lowest speed to reduce air bubbles, 3 to 5 minutes. Let stand, covered with plastic wrap, at room temperature.
No, this is Swiss Meringue buttercream. With Italian Meringue, you would need to heat the water and sugary until syrupy and then add that to the egg whites that is beating in the kitchenaid.
Is this supposed to be for Italian Meringue Buttercream? I watch the clip of them icing the cake and I thought it was Italian Meringue?