Combine egg whites, sugar, water, vanilla, and corn syrup in bowl of standing mixer or large heatproof bowl and set over medium saucepan filled with 1 inch of barely simmering water (do not let bottom of bowl touch water). Cook, stirring constantly, until sugar is dissolved and mixture registers 160°F on instant-read thermometer, 5 to 10 minutes. Remove bowl from heat and transfer mixture to standing mixer fitted with whisk attachment. Beat on medium speed until soft peaks form, about 5 minutes. Increase speed to medium-high and continue to beat until mixture has cooled to room temperature and stiff peaks form, 5 minutes longer. Remove bowl from mixer and use rubber spatula to gently fold in coconut.

Makes 3 cups, enough to frost one 4-layer cake