Whisk together 1/4 cup milk, egg yolks and cornstarch in a large bowl. Heat remaining milk in a heavy saucepan until steaming.

Gradually whisk milk into the egg mixture. Return to the saucepan; cook over medium heat, whisking constantly, until the custard boils and thickens, 1 to 2 minutes. Remove from the heat, stir in vanilla.

Combine egg whites, sugar, cream of tartar and water in a heatproof mixing bowl large enough to fit over the saucepan of simmering hot water.

Set the bowl over the water and beat with an electric mixer at low speed, moving the beaters around the bowl constantly, until an instant-read thermometer registers 140°F (this will take 3 to 5 minutes).

Increase the mixer speed to high and continue beating over the heat for a full 3 1/2 minutes. Remove the bowl from the heat and beat the meringue until cool, about 4 minutes.

Fold the meringue into the egg yolk mixture.

Transfer to a clean bowl and place plastic wrap directly on the surface of the custard to prevent a skin from forming. Set aside to cool slightly.