Place egg whites in a clean, dry bowl of a stand mixer fitted with the whisk attachment.

In a medium saucepan over medium-high heat, bring water, sugar, and cream of tartar to a boil.

Cover and boil 3 minutes.

Insert candy thermometer and boil, without stirring, until temperature reaches 235°F.

Start whipping egg whites on medium speed while the syrup continues to boil.

The egg whites should form stiff, glossy peaks by the same time the syrup reaches 242°F; if not, you can hold the whites by mixing on low until the syrup catches up.

With the mixer on medium, pour the hot syrup into the egg whites. It will spatter, but just keep pouring and mixing.

Once the syrup is incorporated, add the vanilla.

Let the mixer run on medium speed until the frosting reaches room temperature, about 5 to 7 minutes.