Whisk egg yolks and 1/2 cup sugar with a mixer on high speed until pale and thick, about 3 minutes.
Bring milk and vanilla to a boil in a medium saucepan. Remove from heat. Whisk a third of the liquid into egg-yolk mixture. Pour mixture back into pan with remaining hot milk, whisking to combine. Cook over medium heat, stirring constantly, until mixture registers 185 degrees on an instant-read thermometer, 4 to 5 minutes. Strain. Press a piece of plastic wrap directly on the surface, then refrigerate custard until cold.
Beat butter with a mixer on medium-high speed until pale and fluffy, about 3 minutes. With machine running, add cold custard, and beat until combined.
Heat egg whites and remaining 1 cup sugar in a clean heatproof mixer bowl. Set bowl over a pan of simmering water, and whisk constantly until sugar dissolves. Attach bowl to mixer, and whisk on high speed until stiff peaks form.
Add egg-white mixture to butter mixture, and beat on medium-high speed until smooth. Cover, and refrigerate for up to 3 days. (Before using frosting, let it stand at room temperature to warm, then beat on low until smooth again.)
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