Pour about 1/2 cup of water into a medium-sized saucepan and bring to a simmer.
Add egg whites, sugar, cream of tartar, and salt to the bowl of an electric mixer. Whisk with hand-held whisk until the ingredients begin to become foamy.
Place the bowl over the saucepan of simmering water and continue to whisk until the sugar is completely dissolved, about 5 minutes.
Remove the bowl from the saucepan and transfer to a stand mixer with the whisk attachment attached. Turn mixer to medium setting and whip for about 1 minute. Increase the speed to high and whip until stiff peaks are formed, about 5-7 minutes. Reduce speed and incorporate vanilla.
Notes
This makes enough frosting for 2 dozen cupcakes or 1 layer cake.