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Heat milk in a 2 1/2- to 3-quart heavy saucepan over moderate heat until hot but not boiling.
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While milk heats, whisk together yolks, sugar, cornstarch, and salt in a heatproof bowl until smooth.
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Add 1 cup hot milk to yolk mixture in a stream, whisking, then add remaining milk, whisking constantly. Transfer mixture to saucepan and cook over moderately low heat, stirring constantly, until thickened and registers 170°F on thermometer, 6 to 10 minutes (do not boil).
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Immediately force custard through a fine-mesh sieve into a clean bowl and stir in butter and vanilla. Chill custard, its surface covered with wax paper, until cold and thickened, at least 3 hours.