Fill medium saucepan one quarter full with water. Set the saucepan over medium heat, and bring water to a simmer.
Combine egg whites, sugar, and cream of tartar in the heatproof bowl of electric mixer, and place over saucepan. Whisk constantly until sugar is dissolved and whites are warm to the touch, 3 to 3 1/2 minutes.
Transfer bowl to electric mixer fitted with the whisk attachment, and whip, starting on low speed, gradually increasing to high until stiff, glossy peaks form, about 10 minutes. Add vanilla, and mix until combined.