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