Preheat oven to 175 degrees. Put egg whites, sugar, and cream of tartar in a heatproof mixer bowl set over a pan of simmering water. Whisk constantly until egg whites are warm to the touch and sugar is dissolved (test by rubbing the mixture between your fingers), about 3 minutes.
Transfer bowl to mixer; beat on low speed, gradually raising to high, until stiff, glossy peaks form, about 10 minutes. Mix in vanilla.
On parchment-lined baking sheets, pipe meringue into hearts; bake until firm but not brown, 1 to 1 1/2 hours. Let cool on sheets, about 20 minutes.
Let ice cream soften about 5 minutes. Put 1/4 cup ice cream on the flat side of half the meringue hearts. Top with remaining hearts, and freeze sandwiches until ice cream is set, about 15 minutes.
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