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Place the milk in a medium-sized heavy saucepan and set pan over medium heat. Warm milk until very hot, but not boiling.
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While milk is heating, combine the eggs, egg yoks, and salt in a medium mixing bowl. Beat with an electric mixer set to medium speed until thickened, 3 to 4 minutes. With mixer on medium-high, gradually add the sugar (2 to 3 tablespoons at a time), beating 30 seconds after each addition. Continue beating until the mixture is very thick and pale, about 3 minutes more.
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Turn mixer to low and beat in the vanilla and cornstarch, mixing until very smooth. With mixer still on low, gradually add the hot milk—beat in about 1 teaspoon at a time at first, then slowly begin adding more, beating well after each addition.
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Once all the milk has been added, pour the mixture back into the saucepan you used for the milk. Add the cold butter, then set the pan over medium heat. Heat the mixture, stirring constantly with a rubber spatula. When mixture begins to thicken (it will look lumpy), decrease the heat and switch to stirring with a whisk. Continue stirring the mixture gently for another 7 or 8 minutes, until very thick. At this point, reduce heat to very low and cook 1 minute more, stirring with your spatula again.
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Remove from the heat and scrape mixture into a medium mixing bowl. Cover with plastic wrap, pressing the wrap onto the surface of the pastry cream. Cool to room temperature, then refrigerate overnight.