In the heatproof bowl of an electric mixer, combine egg whites, sugar, and vanilla. Set the bowl over a pan of simmering water. Whisk constantly until the sugar has dissolved and whites are hot to the touch, 3 to 5 minutes.
Transfer the bowl to the electric mixer. Using the whisk attachment, mix on low speed, gradually increasing to high speed, until stiff, glossy peaks form, about 10 minutes. Use immediately.