In a heatproof bowl set over (not in) a saucepan of simmering water, combine egg whites, sugar, salt, and water. Cook over medium, stirring constantly, until sugar has dissolved (or mixture registers 150 degrees on an instant-read thermometer), 2 to 3 minutes. Transfer to a large bowl. Using an electric mixer, beat on medium-high until glossy, stiff peaks form (do not overbeat), about 3 minutes; reduce speed to low, add vanilla extract, and beat just until combined. Use immediately.